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Wyświetlanie 1-15 z 32
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:
Variantný prístup k optimalizácii poštovej prepravnej siete
Variant approach to optimization of postal transportation network
Autorzy:
Madleňáková, L.
Madleňák, R.
Powiązania:
https://bibliotekanauki.pl/articles/315566.pdf
Data publikacji:
2013
Wydawca:
Instytut Naukowo-Wydawniczy "SPATIUM"
Tematy:
sieci transportowe
optymalizacja
optymalizacja czasu
teoria grafów
transmission network
time optimization
distance optimization
graph theory
Opis:
Tento článok pojednáva o štruktúre poštovej prepravnej siete a možnostiach jej optimalizácie. Pre potreby optimalizácie poštovej prepravnej siete boli zvolené dva prístupy: optimalizácia na základe času a optimalizácia na základe vzdialenosti s využitím metód teórie grafov. V hlavnej časti článku sú porovnané oba prístupy optimalizácie a v závere zhrnuté základné postuláty vyplývajúce zo špecifík oboch prístupov.
This article discusses about the structure of the transmission network and its optimization options. For the purpose of optimization of postal transport network have been chosen two approaches: optimization on base of the time and optimization on base of the distance with the use of the methods of graph theory. In the main part of the article are compares both approaches of optimization. In theconclusion are summarized the basic postulates arising from the specificities of both approaches.
Źródło:
Autobusy : technika, eksploatacja, systemy transportowe; 2013, 14, 3; 457-464
1509-5878
2450-7725
Pojawia się w:
Autobusy : technika, eksploatacja, systemy transportowe
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Upper bounds on distance vertex irregularity strength of some families of graphs
Autorzy:
Cichacz, Sylwia
Görlich, Agnieszka
Semaničová-Feňovčíková, Andrea
Powiązania:
https://bibliotekanauki.pl/articles/2216229.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
distance vertex irregularity strength of a graph
hypercube
tree
graph
Opis:
For a graph G its distance vertex irregularity strength is the smallest integer k for which one can find a labeling f : V (G) → {1, 2, . . . , k} such that $ \sum_{x \in N(v)} f(x) \neq \sum_{x \in N(u)} f(x) $ for all vertices u, v of G, where N(v) is the open neighborhood of v. In this paper we present some upper bounds on distance vertex irregularity strength of general graphs. Moreover, we give upper bounds on distance vertex irregularity strength of hypercubes and trees.
Źródło:
Opuscula Mathematica; 2022, 42, 4; 561--571
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Union of Distance Magic Graphs
Autorzy:
Cichacz, Sylwia
Nikodem, Mateusz
Powiązania:
https://bibliotekanauki.pl/articles/31342130.pdf
Data publikacji:
2017-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
distance magic labeling
magic constant
sigma labeling
graph labeling
union of graphs
lexicographic product
direct product
Kronecker product
Kotzig array
Opis:
A distance magic labeling of a graph $G = (V,E)$ with $|V | = n$ is a bijection $ \mathcal{l} $ from $V$ to the set ${1, . . ., n}$ such that the weight $ w(x) = \Sigma_{ y \in N_G } (x) \mathcal{l}(y) $ of every vertex $ x \in V $ is equal to the same element $ \mu $, called the magic constant. In this paper, we study unions of distance magic graphs as well as some properties of such graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 1; 239-249
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Distance Magic Index of a Graph
Autorzy:
Godinho, Aloysius
Singh, Tarkeshwar
Arumugam, S.
Powiązania:
https://bibliotekanauki.pl/articles/31342438.pdf
Data publikacji:
2018-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
distance magic labeling
distance magic index
S -magic graph
S -magic labeling
Opis:
Let $G$ be a graph of order $n$ and let $S$ be a set of positive integers with $ |S| = n $. Then $G$ is said to be $S$-magic if there exists a bijection $ \phi : V (G) \rightarrow S $ satisfying $ \Sigma_{ x \in N } (u) \ \phi (x) = k $ (a constant) for every $ u \in V (G) $. Let $ \alpha (S) = \text{max} \{ s : s \in S \} $. Let $ i(G) = \text{min} \ \alpha (S) $, where the minimum is taken over all sets $S$ for which the graph $G$ admits an $S$-magic labeling. Then $ i(G) − n $ is called the distance magic index of the graph $G$. In this paper we determine the distance magic index of trees and complete bipartite graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 1; 135-142
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Rotation and jump distances between graphs
Autorzy:
Chartrand, Gary
Gavlas, Heather
Hevia, Héctor
Johnson, Mark
Powiązania:
https://bibliotekanauki.pl/articles/972022.pdf
Data publikacji:
1997
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
edge rotation
rotation distance
edge jump
jump distance
jump distance graph
Opis:
A graph H is obtained from a graph G by an edge rotation if G contains three distinct vertices u,v, and w such that uv ∈ E(G), uw ∉ E(G), and H = G-uv+uw. A graph H is obtained from a graph G by an edge jump if G contains four distinct vertices u,v,w, and x such that uv ∈ E(G), wx∉ E(G), and H = G-uv+wx. If a graph H is obtained from a graph G by a sequence of edge jumps, then G is said to be j-transformed into H. It is shown that for every two graphs G and H of the same order (at least 5) and same size, G can be j-transformed into H. For every two graphs G and H of the same order and same size, the jump distance $d_j(G,H)$ between G and H is defined as the minimum number of edge jumps required to j-transform G into H. The rotation distance $d_r(G,H)$ between two graphs G and H of the same order and same size is the minimum number of edge rotations needed to transform G into H. The jump and rotation distances of two graphs of the same order and same size are compared. For a set S of graphs of a fixed order at least 5 and fixed size, the jump distance graph $D_j(S)$ of S has S as its vertex set and where G₁ and G₂ in S are adjacent if and only if $d_j(G₁,G₂) = 1$. A graph G is a jump distance graph if there exists a set S of graphs of the same order and same size with $D_j(S) = G$. Several graphs are shown to be jump distance graphs, including all complete graphs, trees, cycles, and cartesian products of jump distance graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 1997, 17, 2; 285-300
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Precise Upper Bound for the Strong Edge Chromatic Number of Sparse Planar Graphs
Autorzy:
Borodin, Oleg V.
Ivanova, Anna O.
Powiązania:
https://bibliotekanauki.pl/articles/30098005.pdf
Data publikacji:
2013-09-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
planar graph
edge coloring
2-distance coloring
strong edgecoloring
Opis:
We prove that every planar graph with maximum degree $ \Delta $ is strong edge $ (2 \Delta − 1)$-colorable if its girth is at least $ 40 [ \frac{\Delta}{2} ] +1 $. The bound $ 2 \Delta −1 $ is reached at any graph that has two adjacent vertices of degree $ \Delta $ .
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 4; 759-770
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Orientation distance graphs revisited
Autorzy:
Goddard, Wayne
Kanakadandi, Kiran
Powiązania:
https://bibliotekanauki.pl/articles/743689.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
orientation
distance graph
arc reversal
Opis:
The orientation distance graph ₒ(G) of a graph G is defined as the graph whose vertex set is the pair-wise non-isomorphic orientations of G, and two orientations are adjacent iff the reversal of one edge in one orientation produces the other. Orientation distance graphs was introduced by Chartrand et al. in 2001. We provide new results about orientation distance graphs and simpler proofs to existing results, especially with regards to the bipartiteness of orientation distance graphs and the representation of orientation distance graphs using hypercubes. We provide results concerning the orientation distance graphs of paths, cycles and other common graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2007, 27, 1; 125-136
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Orientable $ \mathbb{Z}_N $-Distance Magic Graphs
Autorzy:
Cichacz, Sylwia
Freyberg, Bryan
Froncek, Dalibor
Powiązania:
https://bibliotekanauki.pl/articles/31343411.pdf
Data publikacji:
2019-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
distance magic graph
digraph
flow graph
Opis:
Let $ G = (V, E) $ be a graph of order $n$. A distance magic labeling of $G$ is a bijection $ \mathcal{l}: V \rightarrow {1, 2, . . ., n} $ for which there exists a positive integer $k$ such that $ \Sigma_{ x \in N(v) } \mathcal{l} (x) = k $ for all $ v \in V $, where $ N(v) $ is the open neighborhood of $v$. Tuttes flow conjectures are a major source of inspiration in graph theory. In this paper we ask when we can assign $n$ distinct labels from the set $ {1, 2, . . ., n} $ to the vertices of a graph $G$ of order $n$ such that the sum of the labels on heads minus the sum of the labels on tails is constant modulo $n$ for each vertex of $G$. Therefore we generalize the notion of distance magic labeling for oriented graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 2; 533-546
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the uniqueness of $D$-vertex magic constant
Autorzy:
Arumugam, S.
Kamatchi, N.
Vijayakumar, G.R.
Powiązania:
https://bibliotekanauki.pl/articles/30148233.pdf
Data publikacji:
2014-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
distance magic graph
D-vertex magic graph
magic constant
dominating function
fractional domination number
Opis:
Let $G = (V,E)$ be a graph of order n and let $D ⊆ {0, 1, 2, 3, . . .}$. For $v ∈ V$, let $N_D(v) = {u ∈ V : d(u, v) ∈ D}$. The graph $G$ is said to be $D$-vertex magic if there exists a bijection $f : V (G) → {1, 2, . . ., n}$ such that for all $v ∈ V, _{∑uv∈ND(v)} f(u)$ is a constant, called $D$-vertex magic constant. O’Neal and Slater have proved the uniqueness of the $D$-vertex magic constant by showing that it can be determined by the $D$-neighborhood fractional domination number of the graph. In this paper we give a simple and elegant proof of this result. Using this result, we investigate the existence of distance magic labelings of complete $r$-partite graphs where $r ≥ 4$.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 2; 279-286
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Metric Dimension of Directed and Undirected Circulant Graphs
Autorzy:
Vetrík, Tomáš
Powiązania:
https://bibliotekanauki.pl/articles/31870010.pdf
Data publikacji:
2020-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
metric dimension
resolving set
circulant graph
distance
Opis:
The undirected circulant graph $C_n(±1, ±2, . . ., ±t)$ consists of vertices $v_0, v_1, . . ., v_{n−1}$ and undirected edges $v_iv_{i+j}$, where $0 ≤ i ≤ n − 1, 1 ≤ j ≤ t (2 ≤ t ≤ \frac{n}{2})$, and the directed circulant graph $C_n(1, t)$ consists of vertices $v_0, v_1, . . ., v_{n−1}$ and directed edges $v_iv_{i+1}, v_iv_{i+t}$, where $0 ≤ i ≤ n − 1 (2 ≤ t ≤ n−1)$, the indices are taken modulo $n$. Results on the metric dimension of undirected circulant graphs $C_n(±1, ±t)$ are available only for special values of $t$. We give a complete solution of this problem for directed graphs $C_n(1, t)$ for every $t ≥ 2$ if $n ≥ 2t^2$. Grigorious et al. [On the metric dimension of circulant and Harary graphs, Appl. Math. Comput. 248 (2014) 47–54] presented a conjecture saying that dim $(C_n(±1, ±2, . . ., ±t)) = t + p − 1$ for $n = 2tk + t + p$, where $3 ≤ p ≤ t + 1$. We disprove it by showing that dim $(C_n(±1, ±2, . . ., ±t)) ≤ t + \frac{p+1}{2}$ for $n = 2tk + t + p$, where $t ≥ 4$ is even, $p$ is odd, $1 ≤ p ≤ t + 1$ and $k ≥ 1$.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 1; 67-76
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the dimension of Archimedean solids
Autorzy:
Madaras, T.
Siroczki, P.
Powiązania:
https://bibliotekanauki.pl/articles/255658.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Archimedean solid
unit-distance graph
dimension of a graph
Opis:
We study the dimension of graphs of the Archimedean solids. For most of these graphs we find the exact value of their dimension by finding unit-distance embeddings in the euclidean plane or by proving that such an embedding is not possible.
Źródło:
Opuscula Mathematica; 2014, 34, 1; 123-138
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Determinant of q-Distance Matrix of a Graph
Autorzy:
Li, Hong-Hai
Su, Li
Zhang, Jing
Powiązania:
https://bibliotekanauki.pl/articles/30147229.pdf
Data publikacji:
2014-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
q-distance matrix
determinant
weighted graph
directed graph
Opis:
In this note, we show how the determinant of the q-distance matrix Dq(T) of a weighted directed graph G can be expressed in terms of the corresponding determinants for the blocks of G, and thus generalize the results obtained by Graham et al. [R.L. Graham, A.J. Hoffman and H. Hosoya, On the distance matrix of a directed graph, J. Graph Theory 1 (1977) 85-88]. Further, by means of the result, we determine the determinant of the q-distance matrix of the graph obtained from a connected weighted graph G by adding the weighted branches to G, and so generalize in part the results obtained by Bapat et al. [R.B. Bapat, S. Kirkland and M. Neumann, On distance matrices and Laplacians, Linear Algebra Appl. 401 (2005) 193- 209]. In particular, as a consequence, determinantal formulae of q-distance matrices for unicyclic graphs and one class of bicyclic graphs are presented.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 1; 103-111
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Some Characterizations of Antipodal Partial Cubes
Autorzy:
Polat, Norbert
Powiązania:
https://bibliotekanauki.pl/articles/31343441.pdf
Data publikacji:
2019-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
diametrical graph
harmonic graph
antipodal graph
distance-balanced graph
partial cube
pre-hull number
Opis:
We prove that any harmonic partial cube is antipodal, which was conjectured by Fukuda and K. Handa, Antipodal graphs and oriented matroids, Discrete Math. 111 (1993) 245–256. Then we prove that a partial cube G is antipodal if and only if the subgraphs induced by Wab and Wba are isomorphic for every edge ab of G. This gives a positive answer to a question of Klavžar and Kovše, On even and harmonic-even partial cubes, Ars Combin. 93 (2009) 77–86. Finally we prove that the distance-balanced partial cube that are antipodal are those whose pre-hull number is at most 1.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 2; 439-453
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Minimal Graphs with Respect to Geometric Distance Realizability
Autorzy:
Madaras, Tomáš
Široczki, Pavol
Powiązania:
https://bibliotekanauki.pl/articles/32083776.pdf
Data publikacji:
2021-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
unit-distance graph
odd-distance graph
Euclidean plane
Opis:
A graph G is minimal non-unit-distance graph if there is no drawing of G in Euclidean plane having all edges of unit length, but, for each edge e of G, G − e has such a drawing. We prove that, for infinitely many n, the number of non-isomorphic n-vertex minimal non-unit-distance graphs is at least exponential in n.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 1; 65-73
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 32

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