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Tytuł:
Wiener index of strong product of graphs
Autorzy:
Peterin, I.
Zigert-Pletersek, P.
Powiązania:
https://bibliotekanauki.pl/articles/255704.pdf
Data publikacji:
2018
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Wiener index
graph product
strong product
Opis:
The Wiener index of a connected graph G is the sum of distances between all pairs of vertices of G. The strong product is one of the four most investigated graph products. In this paper the general formula for the Wiener index of the strong product of connected graphs is given. The formula can be simplified if both factors are graphs with the constant eccentricity. Consequently, closed formulas for the Wiener index of the strong product of a connected graph G of constant eccentricity with a cycle are derived.
Źródło:
Opuscula Mathematica; 2018, 38, 1; 81-94
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Inverse Problem on the Steiner Wiener Index
Autorzy:
Li, Xueliang
Mao, Yaping
Gutman, Ivan
Powiązania:
https://bibliotekanauki.pl/articles/31342440.pdf
Data publikacji:
2018-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
distance
Steiner distance
Wiener index
Steiner Wiener index
Opis:
The Wiener index $ W(G) $ of a connected graph $G$, introduced by Wiener in 1947, is defined as $ W(G) = \Sigma_{ u,v \in V (G) } \ d_G(u, v) $, where $ d_G(u, v) $ is the distance (the length a shortest path) between the vertices $u$ and $v$ in $G$. For $ S \subseteq V (G) $, the Steiner distance $d(S)$ of the vertices of $S$, introduced by Chartrand et al. in 1989, is the minimum size of a connected subgraph of $G$ whose vertex set contains $S$. The $k$-th Steiner Wiener index $ SW_k(G) $ of $G$ is defined as $ SW_k(G)= \Sigma_{ S \subseteq V(G) \ |S|=k } \ d(S) $. We investigate the following problem: Fixed a positive integer $k$, for what kind of positive integer w does there exist a connected graph $G$ (or a tree $T$) of order $ n \ge k$ such that $ SW_k(G) = w$ (or $ SW_k(T) = w$)? In this paper, we give some solutions to this problem.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 1; 83-95
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Steiner Wiener Index of A Graph
Autorzy:
Li, Xueliang
Mao, Yaping
Gutman, Ivan
Powiązania:
https://bibliotekanauki.pl/articles/31340916.pdf
Data publikacji:
2016-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
distance
Steiner distance
Wiener index
Steiner Wiener k- index
Opis:
The Wiener index $ W(G) $ of a connected graph $G$, introduced by Wiener in 1947, is defined as $ W(G) = \Sigma_{ u,v \in V(G) } d(u, v) $ where $ d_G(u, v) $ is the distance between vertices $u$ and $v$ of $G$. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least 2 and $ S \subseteq V (G) $, the Steiner distance $d(S)$ of the vertices of $S$ is the minimum size of a connected subgraph whose vertex set is $S$. We now introduce the concept of the Steiner Wiener index of a graph. The Steiner k-Wiener index $ SW_k(G) $ of $ G $ is defined by $ \Sigma_{ S \subseteq V(G) \ |S| = k } \ d(S) $. Expressions for $ SW_k $ for some special graphs are obtained. We also give sharp upper and lower bounds of $ SW_k $ of a connected graph, and establish some of its properties in the case of trees. An application in chemistry of the Steiner Wiener index is reported in our another paper.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 2; 455-465
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Wiener index of generalized stars and their quadratic line graphs
Autorzy:
Dobrynin, Andrey
Mel'nikov, Leonid
Powiązania:
https://bibliotekanauki.pl/articles/743914.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
distance in a graph
Wiener index
star
iterated line graph
Opis:
The Wiener index, W, is the sum of distances between all pairs of vertices in a graph G. The quadratic line graph is defined as L(L(G)), where L(G) is the line graph of G. A generalized star S is a tree consisting of Δ ≥ 3 paths with the unique common endvertex. A relation between the Wiener index of S and of its quadratic graph is presented. It is shown that generalized stars having the property W(S) = W(L(L(S)) exist only for 4 ≤ Δ ≤ 6. Infinite families of generalized stars with this property are constructed.
Źródło:
Discussiones Mathematicae Graph Theory; 2006, 26, 1; 161-175
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Wiener index of the tensor product of a path and a cycle
Autorzy:
Pattabiraman, K.
Paulraja, P.
Powiązania:
https://bibliotekanauki.pl/articles/743591.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
tensor product
Wiener index
Opis:
The Wiener index, denoted by W(G), of a connected graph G is the sum of all pairwise distances of vertices of the graph, that is, $W(G) = ½Σ_{u,v ∈ V(G)} d(u,v)$. In this paper, we obtain the Wiener index of the tensor product of a path and a cycle.
Źródło:
Discussiones Mathematicae Graph Theory; 2011, 31, 4; 737-751
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Gutman Index and the Edge-Wiener Index of Graphs with Given Vertex-Connectivity
Autorzy:
Mazorodze, Jaya Percival
Mukwembi, Simon
Vetrík, Tomáš
Powiązania:
https://bibliotekanauki.pl/articles/31340463.pdf
Data publikacji:
2016-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Gutman index
edge-Wiener index
vertex-connectivity
Opis:
The Gutman index and the edge-Wiener index have been extensively investigated particularly in the last decade. An important stream of re- search on graph indices is to bound indices in terms of the order and other parameters of given graph. In this paper we present asymptotically sharp upper bounds on the Gutman index and the edge-Wiener index for graphs of given order and vertex-connectivity κ, where κ is a constant. Our results substantially generalize and extend known results in the area.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 4; 867-876
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Wiener and vertex PI indices of the strong product of graphs
Autorzy:
Pattabiraman, K.
Paulraja, P.
Powiązania:
https://bibliotekanauki.pl/articles/743324.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
strong product
Wiener index
hyper-Wiener index
vertex PI index
Opis:
The Wiener index of a connected graph G, denoted by W(G), is defined as $½ ∑_{u,v ∈ V(G)}d_G(u,v)$. Similarly, the hyper-Wiener index of a connected graph G, denoted by WW(G), is defined as $½W(G) + ¼ ∑_{u,v ∈ V(G)} d²_G(u,v)$. The vertex Padmakar-Ivan (vertex PI) index of a graph G is the sum over all edges uv of G of the number of vertices which are not equidistant from u and v. In this paper, the exact formulae for Wiener, hyper-Wiener and vertex PI indices of the strong product $G ⊠ K_{m₀,m₁,...,m_{r -1}}$, where $K_{m₀,m₁,...,m_{r -1}}$ is the complete multipartite graph with partite sets of sizes $m₀,m₁, ...,m_{r -1}$, are obtained. Also lower bounds for Wiener and hyper-Wiener indices of strong product of graphs are established.
Źródło:
Discussiones Mathematicae Graph Theory; 2012, 32, 4; 749-769
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
p-Wiener intervals and p-Wiener free intervals
Autorzy:
Kathiresan, Kumarappan
Arockiaraj, S.
Powiązania:
https://bibliotekanauki.pl/articles/743709.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Wiener index of a graph
Wiener graphical
p-Wiener interval
p-Wiener free interval
hyper-Wiener index of a graph
radius
diameter
Opis:
A positive integer n is said to be Wiener graphical, if there exists a graph G with Wiener index n. In this paper, we prove that any positive integer n(≠ 2,5) is Wiener graphical. For any positive integer p, an interval [a,b] is said to be a p-Wiener interval if for each positive integer n ∈ [a,b] there exists a graph G on p vertices such that W(G) = n. For any positive integer p, an interval [a,b] is said to be p-Wiener free interval (p-hyper-Wiener free interval) if there exist no graph G on p vertices with a ≤ W(G) ≤ b (a ≤ WW(G) ≤ b). In this paper, we determine some p-Wiener intervals and p-Wiener free intervals for some fixed positive integer p.
Źródło:
Discussiones Mathematicae Graph Theory; 2012, 32, 1; 121-127
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Notes on topological indices of graph and its complement
Autorzy:
Madaras, T.
Mockovciakova, M.
Powiązania:
https://bibliotekanauki.pl/articles/254698.pdf
Data publikacji:
2013
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Wiener index
Zagreb index
Randic index
bipartite graph
bipartite complement
Opis:
In this note, we derive the lower bound on the sum for Wiener index of bipartite graph and its bipartite complement, as well as the lower and upper bounds on this sum for the Randić index and Zagreb indices. We also discuss the quality of these bounds.
Źródło:
Opuscula Mathematica; 2013, 33, 1; 107-115
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Eccentric distance sum index for some classes of connected graphs
Autorzy:
Bielak, Halina
Broniszewska, Katarzyna
Powiązania:
https://bibliotekanauki.pl/articles/746990.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Adjacent eccentric distance sum
diameter
distance
eccentricity
radius
Wiener index
Opis:
In this paper we show some properties of the eccentric distance sum index which is defined as follows \(\xi^{d}(G)=\sum_{v \in V(G)}D(v) \varepsilon(v)\). This index is widely used by chemists and biologists in their researches. We present a lower bound of this index for a new class of graphs.
Źródło:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2017, 71, 2
0365-1029
2083-7402
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The use of phytoplankton communities for assessment of water quality in the Wadaslintang Reservoir in Indonesia
Autorzy:
Piranti, Agatha S.
Wibowo, Dwi N.
Powiązania:
https://bibliotekanauki.pl/articles/946893.pdf
Data publikacji:
2020
Wydawca:
Instytut Technologiczno-Przyrodniczy
Tematy:
algae
pollution level
Shannon-Wiener index
Storet index
water quality
Opis:
The use of phytoplankton as an indicator of water pollution is a promising tool for assessment of water quality. The purpose of this study was to determine whether diversity indices, including the species richness and diversity of phyto-plankton, could be used for reliable assessment of water quality in the Wadaslintang Reservoir in Indonesia. Surveys were conducted monthly at eight sites, from July 2019 to October 2019. Phytoplankton was collected during the day at 10:00 until approximately 15:00 in the euphotic zone. The parameters investigated were species richness and the abundance of phytoplankton, as well as water quality parameters listed in Government Regulation Number 82 of 2001. The level of pollution was represented biologically by the Shannon–Wiener diversity index and physicochemically by the STORET (storage and retrieval of water quality data) index. Moreover, the two indices were compared to determine whether a particular diversity index was more effective for assessment of this reservoir. The results showed that during the dry season, 22 taxa of phytoplankton were present, belonging to Cyanophyta, Chlorophyta, Chrysophyta, and Euglenophyta. During the wet season, 29 taxa were found, belonging to Cyanophyta, Chlorophyta, and Chrysophyta. Based on the Shannon-Wiener index and STORET index, water quality was better during the wet season than during the dry season. The results of water quality assessment using both indices were consistent, but the diversity index was a more sensitive indicator of pollution levels. Therefore, the Shannon–Wiener index is a useful tool for assessment of water quality in the Wadaslintang Reservoir.
Źródło:
Journal of Water and Land Development; 2020, 46; 170-178
1429-7426
2083-4535
Pojawia się w:
Journal of Water and Land Development
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Impact of Jute Retting on Native Fish Diversity and Aquatic Health of Roadside Transitory Water Bodies: an Assessment in Eastern India
Autorzy:
Ghosh, D.
Biswas, J. K.
Powiązania:
https://bibliotekanauki.pl/articles/125476.pdf
Data publikacji:
2015
Wydawca:
Polskie Towarzystwo Inżynierii Ekologicznej
Tematy:
transitory water bodies
physicochemical analysis
fish diversity
Shannon-Wiener Index
jute retting
Opis:
Roadside transitory water bodies being manmade depressions have a great ecological and socio-economic importance from years. The effects of agricultural runoffs, jute retting, macro-phytes infestations and inadequate rainfall in changed climate often degrade transitory water bodies’ environment while the biodiversity have impacted severely because of population pressure, over exploitation and indiscriminate use of fine meshed fishing gears as a whole. Physico-chemical and biological analysis with fish species composition, relative abundance, diversity indices like species richness, evenness and Shannon-Wiener index were carried out for pre-, during and post-jute retting season and for year mean as a whole to assess impact of jute retting on the roadside transitory water body’s environmental health and indigenous fish diversity at Sahebnagar village in Nadia District, India. All the physico-chemical parameters barring biochemical oxygen demand and water transparency remained more or less same or marginally got little changed during those three seasons. As much as 19 native fish species with varied relative abundances and dominances were identified. Jute retting impacted lower native fish diversity indices like Shannon-Wiener index values (1.94 to 2.68) clearly indicated poor to moderate pollution status of the transitory water body in that area during monsoon in particular and throughout the year in general. So we opined there should be some control over the intense jute retting in the road side transitory water bodies for sustainable management of these manmade resources.
Źródło:
Journal of Ecological Engineering; 2015, 16, 4; 14-21
2299-8993
Pojawia się w:
Journal of Ecological Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Schultz and Modified Schultz Polynomials of Coronene Polycyclic Aromatic Hydrocarbons
Autorzy:
Farahani, M. R.
Powiązania:
https://bibliotekanauki.pl/articles/412400.pdf
Data publikacji:
2014
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
topological Indices
Schultz Polynomial
Hosoya Polynomial
Wiener Index
coronene
polycyclic aromatic hydrocarbons
PAHs
Opis:
Let G = (V;E) be a simple connected graph. The sets of vertices and edges of G are denoted by V = V(G) and E = E(G), respectively. In such a simple molecular graph, vertices represent atoms and edges represent bonds. The distance between the vertices u and v in V(G) of graph G is the number of edges in a shortest path connecting them, we denote by d(u,v). In graph theory, we have many invariant polynomials for a graph G. In this research, we computing the Schultz polynomial, Modified Schultz polynomial, Hosoya polynomial and their topological indices of a Hydrocarbon molecule, that we call “Coronene Polycyclic Aromatic Hydrocarbons”.
Źródło:
International Letters of Chemistry, Physics and Astronomy; 2014, 13, 1; 1-10
2299-3843
Pojawia się w:
International Letters of Chemistry, Physics and Astronomy
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Use of the Shannon Wiener index to measure LAG diversity, a major player in regional rural development
Wykorzystanie indeksu Shannon Wiener do pomiaru różnorodności LAGów, głównego gracza rozwoju obszarów wiejskich regionów
Autorzy:
Pártlová, Petra
Vachal, Jan
Dobrovič, Ján
Tabor, Joanna
Powiązania:
https://bibliotekanauki.pl/articles/1830687.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska
Tematy:
diversification
cluster
Shannon-Wiener index
regional development
Local Action Group
LAG
dywersyfikacja
klaster
indeks Shannona-Wienera
rozwój regionalny
Lokalna Grupa Działania
LGD
Opis:
The article presents a new scientific approach to the issue of entropy as a pro-growth and limiting factor in regional development and its practical elaboration. The research goal was to formulate a theoretical definition of entropy in regional development and to verify it in practice, i.e. to diagnose the entropy factor and to effectively analyze it with the possibility of its practical use. The use of the Shannon Wiener index for Local Action Groups in the South Bohemian region has provided valid results in the field of differentiation of territorial units, such as Local Action Groups (LAGs), regions and municipalities, as well as an appropriate basis for prediction of their further development. The research has also confirmed suitability of four main indication pillars (economic, infrastructure, social and environmental) while their indicators should be adjusted to the character of the tested territory. An appropriate approach seems to be application of the entropy index to a relatively closed unit where the elements mutually affect one another and have mutual relations and ties. Outputs from the solution can be seen as a description of the general status in the individual LAGs; moreover, outputs from the research have been examined by LAG managements and they have seen them as an important source of knowledge and have made some recommendations to strengthen their informative capacity. In conformity with the findings we can conclude that the achieved results should be seen as the first approximation of the solution of the concerned issue and they need to be further verified and completed.
W artykule przedstawiono nowe naukowe podejście do zagadnienia entropii jako czynnika prorozwojowego i ograniczającego rozwój regionalny oraz jego praktyczne opracowanie. Celem badań było sformułowanie teoretycznej definicji entropii w rozwoju regionalnym i zweryfikowanie jej w praktyce, tj. Zdiagnozowanie czynnika entropii i efektywna analiza z możliwością jej praktycznego wykorzystania. Zastosowanie indeksu Shannona Wienera dla lokalnych grup działania w regionie południowoczeskim dostarczyło wiarygodnych wyników w zakresie zróżnicowania jednostek terytorialnych, takich jak lokalne grupy działania (LGD), regiony i gminy, a także odpowiednią podstawę do prognozowania ich dalszego rozwoju. Badania potwierdziły również przydatność czterech głównych filarów wskazań (ekonomiczny, infrastrukturalny, społeczny i środowiskowy), a ich wskaźniki powinny być dostosowane do charakteru badanego terenu. Wydaje się, że właściwym podejściem jest zastosowanie wskaźnika entropii do stosunkowo zamkniętej jednostki, w której elementy wzajemnie na siebie oddziałują i mają wzajemne relacje i więzi. Wyniki rozwiązania można postrzegać jako opis ogólnego stanu poszczególnych LGD; ponadto wyniki badań zostały przeanalizowane przez kierownictwo LGD i uznały je za ważne źródło wiedzy i sformułowały zalecenia w celu wzmocnienia ich zdolności informacyjnej. Zgodnie z ustaleniami można stwierdzić, że uzyskane wyniki należy traktować jako pierwsze przybliżenie rozwiązania rozpatrywanej kwestii i wymagają dalszej weryfikacji i uzupełnienia.
Źródło:
Polish Journal of Management Studies; 2020, 22, 1; 385-400
2081-7452
Pojawia się w:
Polish Journal of Management Studies
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Few Examples and Counterexamples in Spectral Graph Theory
Autorzy:
Stevanović, Dragan
Milosavljević, Nikola
Vukičević, Damir
Powiązania:
https://bibliotekanauki.pl/articles/31563587.pdf
Data publikacji:
2020-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
communicability distance
spectral radius
integral graph
second Zagreb index
Wiener index
estrada index
almost cospectral graphs
NEPS of graphs
Opis:
We present a small collection of examples and counterexamples for selected problems, mostly in spectral graph theory, that have occupied our minds over a number of years without being completely resolved.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 2; 637-662
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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