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    Wyświetlanie 1-11 z 11
    Tytuł:
    Packing Coloring of Some Undirected and Oriented Coronae Graphs
    Autorzy:
    Laïche, Daouya
    Bouchemakh, Isma
    Sopena, Éric
    Powiązania:
    https://bibliotekanauki.pl/articles/31341695.pdf
    Data publikacji:
    2017-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    packing coloring
    packing chromatic number
    corona graph
    path
    cycle
    Opis:
    The packing chromatic number χρ(G) of a graph G is the smallest integer k such that its set of vertices V(G) can be partitioned into k disjoint subsets V1, . . ., Vk, in such a way that every two distinct vertices in Vi are at distance greater than i in G for every i, 1 ≤ i ≤ k. For a given integer p ≥ 1, the p-corona of a graph G is the graph obtained from G by adding p degree-one neighbors to every vertex of G. In this paper, we determine the packing chromatic number of p-coronae of paths and cycles for every p ≥ 1. Moreover, by considering digraphs and the (weak) directed distance between vertices, we get a natural extension of the notion of packing coloring to digraphs. We then determine the packing chromatic number of orientations of p-coronae of paths and cycles.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 3; 665-690
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs
    Autorzy:
    Dettlaff, M.
    Raczek, J.
    Yero, I. G.
    Powiązania:
    https://bibliotekanauki.pl/articles/255785.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    domination
    paired domination
    independent domination
    edge subdivision
    edge multisubdivision
    corona graph
    Opis:
    Given a graph G = (V, E), the subdivision of an edge e = uv ∈ E(G) means the substitution of the edge e by a vertex x and the new edges ux and xv. The domination subdivision number of a graph G is the minimum number of edges of G which must be subdivided (where each edge can be subdivided at most once) in order to increase the domination number. Also, the domination multisubdivision number of G is the minimum number of subdivisions which must be done in one edge such that the domination number increases. Moreover, the concepts of paired domination and independent domination subdivision (respectively multisubdivision) numbers are denned similarly. In this paper we study the domination, paired domination and independent domination (subdivision and multisubdivision) numbers of the generalized corona graphs.
    Źródło:
    Opuscula Mathematica; 2016, 36, 5; 575-588
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Equitable Coloring of Graphs. Recent Theoretical Results and New Practical Algorithms
    Autorzy:
    Furmańczyk, H.
    Jastrzębski, A.
    Kubale, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/230069.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    computer experiments
    corona graph
    equitable chromatic number
    equitable coloring conjectures
    NP-hardness
    polynomial heuristics
    Opis:
    In many applications in sequencing and scheduling it is desirable to have an underlaying graph as equitably colored as possible. In this paper we survey recent theoretical results concerning conditions for equitable colorability of some graphs and recent theoretical results concerning the complexity of equitable coloring problem. Next, since the general coloring problem is strongly NP-hard, we report on practical experiments with some efficient polynomial-time algorithms for approximate equitable coloring of general graphs.
    Źródło:
    Archives of Control Sciences; 2016, 26, 3; 281-295
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Equitable Colorings Of Corona Multiproducts Of Graphs
    Autorzy:
    Furmánczyk, Hanna
    Kubale, Marek
    Mkrtchyan, Vahan V.
    Powiązania:
    https://bibliotekanauki.pl/articles/31341573.pdf
    Data publikacji:
    2017-11-27
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    corona graph
    equitable chromatic number
    equitable coloring conjecture
    equitable graph coloring
    multiproduct of graphs
    NP-completeness
    polynomial algorithm
    Opis:
    A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by χ=(G). It is known that the problem of computation of χ=(G) is NP-hard in general and remains so for corona graphs. In this paper we consider the same model of coloring in the case of corona multiproducts of graphs. In particular, we obtain some results regarding the equitable chromatic number for the l-corona product G ◦l H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs are mostly constructive in that they lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G. Moreover, we confirm the Equitable Coloring Conjecture for corona products of such graphs. This paper extends the results from [H. Furmánczyk, K. Kaliraj, M. Kubale and V.J. Vivin, Equitable coloring of corona products of graphs, Adv. Appl. Discrete Math. 11 (2013) 103–120].
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 4; 1079-1094
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Spectra Of Variants Of The Corona Of Two Graphs And Some New Equienergetic Graphs
    Autorzy:
    Adiga, Chandrashekar
    Rakshith, B.R.
    Powiązania:
    https://bibliotekanauki.pl/articles/31341147.pdf
    Data publikacji:
    2016-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    spectrum
    corona
    neighbourhood corona
    edge corona
    energy of a graph
    equienergetic graphs
    Opis:
    Let G and H be two graphs. The join G ∨ H is the graph obtained by joining every vertex of G with every vertex of H. The corona G ○ H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining the i-th vertex of G to every vertex in the i-th copy of H. The neighborhood corona G★H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining the neighbors of the i-th vertex of G to every vertex in the i-th copy of H. The edge corona G ◇ H is the graph obtained by taking one copy of G and |E(G)| copies of H and joining each terminal vertex of i-th edge of G to every vertex in the i-th copy of H. Let G1, G2, G3 and G4 be regular graphs with disjoint vertex sets. In this paper we compute the spectrum of (G1 ∨ G2) ∪ (G1 ★ G3), (G1 ∨ G2) ∪ (G2 ★ G3) ∪ (G1 ★ G4), (G1 ∨ G2) ∪ (G1 ○ G3), (G1 ∨ G2) ∪ (G2 ○ G3) ∪ (G1 ○ G4), (G1 ∨ G2) ∪ (G1 ◇ G3), (G1 ∨ G2) ∪ (G2 ◇ G3) ∪ (G1 ◇ G4), (G1 ∨ G2) ∪ (G2 ○ G3) ∪ (G1 ★ G3), (G1 ∨ G2) ∪ (G2 ○ G3) ∪ (G1 ◇ G4) and (G1 ∨ G2) ∪ (G2 ★ G3) ∪ (G1 ◇ G4). As an application, we show that there exist some new pairs of equienergetic graphs on n vertices for all n ≥ 11.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2016, 36, 1; 127-140
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Introduction to dominated edge chromatic number of a graph
    Autorzy:
    Piri, Mohammad R.
    Alikhani, Saeid
    Powiązania:
    https://bibliotekanauki.pl/articles/2051020.pdf
    Data publikacji:
    2021
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    dominated edge chromatic number
    subdivision
    operation
    corona
    Opis:
    We introduce and study the dominated edge coloring of a graph. A dominated edge coloring of a graph $G$, is a proper edge coloring of $G$ such that each color class is dominated by at least one edge of $G$. The minimum number of colors among all dominated edge coloring is called the dominated edge chromatic number, denoted by $\chi_{dom}^{\prime}(G)$. We obtain some properties of $\chi_{dom}^{\prime}(G)$ and compute it for specific graphs. Also examine the effects on $\chi_{dom}^{\prime}(G)$ when $G$ is modified by operations on vertex and edge of G. Finally, we consider the k-subdivision of G and study the dominated edge chromatic number of these kind of graphs.
    Źródło:
    Opuscula Mathematica; 2021, 41, 2; 245-257
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Accurate Domination in Graphs
    Autorzy:
    Cyman, Joanna
    Henning, Michael A.
    Topp, Jerzy
    Powiązania:
    https://bibliotekanauki.pl/articles/31343372.pdf
    Data publikacji:
    2019-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    domination number
    accurate domination number
    tree
    corona
    Opis:
    A dominating set of a graph G is a subset D ⊆ VG such that every vertex not in D is adjacent to at least one vertex in D. The cardinality of a smallest dominating set of G, denoted by γ(G), is the domination number of G. The accurate domination number of G, denoted by γa(G), is the cardinality of a smallest set D that is a dominating set of G and no |D|-element subset of VG \ D is a dominating set of G. We study graphs for which the accurate domination number is equal to the domination number. In particular, all trees G for which γa(G) = γ(G) are characterized. Furthermore, we compare the accurate domination number with the domination number of different coronas of a graph.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2019, 39, 3; 615-627
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Computing the Metric Dimension of a Graph from Primary Subgraphs
    Autorzy:
    Kuziak, Dorota
    Rodríguez-Velázquez, Juan A.
    Yero, Ismael G.
    Powiązania:
    https://bibliotekanauki.pl/articles/31342126.pdf
    Data publikacji:
    2017-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    metric dimension
    metric basis
    primary subgraphs
    rooted product graphs
    corona product graphs
    Opis:
    Let G be a connected graph. Given an ordered set W = {w1, . . ., wk} ⊆ V (G) and a vertex u ∈ V (G), the representation of u with respect to W is the ordered k-tuple (d(u, w1), d(u, w2), . . ., d(u, wk)), where d(u, wi) denotes the distance between u and wi. The set W is a metric generator for G if every two different vertices of G have distinct representations. A minimum cardinality metric generator is called a metric basis of G and its cardinality is called the metric dimension of G. It is well known that the problem of finding the metric dimension of a graph is NP-hard. In this paper we obtain closed formulae for the metric dimension of graphs with cut vertices. The main results are applied to specific constructions including rooted product graphs, corona product graphs, block graphs and chains of graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 1; 273-293
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Equitable Total Coloring of Corona of Cubic Graphs
    Autorzy:
    Furmańczyk, Hanna
    Zuazua, Rita
    Powiązania:
    https://bibliotekanauki.pl/articles/32361758.pdf
    Data publikacji:
    2021-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    equitable coloring
    total coloring
    equitable total coloring
    cubic graphs
    Opis:
    The minimum number of total independent partition sets of V∪E of a graph G = (V, E) is called the total chromatic number of G, denoted by χ'′(G). If the difference between cardinalities of any two total independent sets is at most one, then the minimum number of total independent partition sets of V∪E is called the equitable total chromatic number, and is denoted by χ'′=(G). In this paper we consider equitable total coloring of coronas of cubic graphs, G◦H. It turns out that independently on the values of equitable total chromatic number of factors G and H, equitable total chromatic number of corona G◦H is equal to Δ(G◦H)+1. Thereby, we confirm Total Coloring Conjecture (TCC), posed by Behzad in 1964, and Equitable Total Coloring Conjecture (ETCC), posed by Wang in 2002, for coronas of cubic graphs. As a direct consequence we get that all coronas of cubic graphs are of Type 1.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 4; 1147-1163
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The General Position Problem on Kneser Graphs and on Some Graph Operations
    Autorzy:
    Ghorbani, Modjtaba
    Maimani, Hamid Reza
    Momeni, Mostafa
    Mahid, Farhad Rahimi
    Klavžar, Sandi
    Rus, Gregor
    Powiązania:
    https://bibliotekanauki.pl/articles/32222714.pdf
    Data publikacji:
    2021-11-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    general position set
    Kneser graphs
    Cartesian product of graphs
    corona over graphs
    line graphs
    Opis:
    A vertex subset S of a graph G is a general position set of G if no vertex of S lies on a geodesic between two other vertices of S. The cardinality of a largest general position set of G is the general position number (gp-number) gp(G) of G. The gp-number is determined for some families of Kneser graphs, in particular for K(n, 2), n ≥ 4, and K(n, 3), n ≥ 9. A sharp lower bound on the gp-number is proved for Cartesian products of graphs. The gp-number is also determined for joins of graphs, coronas over graphs, and line graphs of complete graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2021, 41, 4; 1199-1213
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Graphs with Clusters Perturbed by Regular Graphs—Aα-Spectrum and Applications
    Autorzy:
    Cardoso, Domingos M.
    Pastén, Germain
    Rojo, Oscar
    Powiązania:
    https://bibliotekanauki.pl/articles/31546556.pdf
    Data publikacji:
    2020-05-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    cluster
    convex combination of matrices
    corona product of graphs
    Aα-spectrum
    Opis:
    Given a graph G, its adjacency matrix A(G) and its diagonal matrix of vertex degrees D(G), consider the matrix Aα(G) = αD(G) + (1 − α)A(G), where α ∈ [0, 1). The Aα -spectrum of G is the multiset of eigenvalues of Aα(G) and these eigenvalues are the α-eigenvalues of G. A cluster in G is a pair of vertex subsets (C, S), where C is a set of cardinality |C| ≥ 2 of pairwise co-neighbor vertices sharing the same set S of |S| neighbors. Assuming that G is connected and it has a cluster (C, S), G(H) is obtained from G and an r-regular graph H of order |C| by identifying its vertices with the vertices in C, eigenvalues of Aα(G) and Aα(G(H)) are deduced and if Aα(H) is positive semidefinite, then the i-th eigenvalue of Aα(G(H)) is greater than or equal to i-th eigenvalue of Aα(G). These results are extended to graphs with several pairwise disjoint clusters (C1, S1), . . ., (Ck, Sk). As an application, the effect on the energy, α-Estrada index and α-index of a graph G with clusters when the edges of regular graphs are added to G are analyzed. Finally, the Aα-spectrum of the corona product G ◦ H of a connected graph G and a regular graph H is determined.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 2; 451-466
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-11 z 11

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