Autor: MacGillivray, Gary - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Structure of the set of all minimal total dominating functions of some classes of graphs
Autorzy:: Kumar, K.
MacGillivray, Gary
Powiązania:: https://bibliotekanauki.pl/articles/744030.pdf
Data publikacji:: 2010
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: minimal total dominating functions (MTDFs)
convex combination of MTDFs
basic minimal total dominating functions (BMTDFs)
simplex
polytope
simplicial complex
function separable graphs
function reducible graphs
Opis:: In this paper we study some of the structural properties of the set of all minimal total dominating functions ($_T$) of cycles and paths and introduce the idea of function reducible graphs and function separable graphs. It is proved that a function reducible graph is a function separable graph. We shall also see how the idea of function reducibility is used to study the structure of $_T(G)$ for some classes of graphs.
Źródło:: Discussiones Mathematicae Graph Theory; 2010, 30, 3; 407-423
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Analogues of cliques for oriented coloring
Autorzy:: Klostermeyer, William
MacGillivray, Gary
Powiązania:: https://bibliotekanauki.pl/articles/744524.pdf
Data publikacji:: 2004
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: graph coloring
oriented coloring
clique
planar graph
Opis:: We examine subgraphs of oriented graphs in the context of oriented coloring that are analogous to cliques in traditional vertex coloring. Bounds on the sizes of these subgraphs are given for planar, outerplanar, and series-parallel graphs. In particular, the main result of the paper is that a planar graph cannot contain an induced subgraph D with more than 36 vertices such that each pair of vertices in D are joined by a directed path of length at most two.
Źródło:: Discussiones Mathematicae Graph Theory; 2004, 24, 3; 373-387
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Eternal Domination: Criticality and Reachability
Autorzy:: Klostermeyer, William F.
MacGillivray, Gary
Powiązania:: https://bibliotekanauki.pl/articles/31342174.pdf
Data publikacji:: 2017-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: dominating set
eternal dominating set
critical graphs
Opis:: We show that for every minimum eternal dominating set, D, of a graph G and every vertex v ∈ D, there is a sequence of attacks at the vertices of G which can be defended in such a way that an eternal dominating set not containing v is reached. The study of the stronger assertion that such a set can be reached after a single attack is defended leads to the study of graphs which are critical in the sense that deleting any vertex reduces the eternal domination number. Examples of these graphs and tight bounds on connectivity, edge-connectivity and diameter are given. It is also shown that there exist graphs in which deletion of any edge increases the eternal domination number, and graphs in which addition of any edge decreases the eternal domination number.
Źródło:: Discussiones Mathematicae Graph Theory; 2017, 37, 1; 63-77
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: Reconfiguring Minimum Dominating Sets: The γ-Graph of a Tree
Autorzy:: Edwards, Michelle
MacGillivray, Gary
Nasserasr, Shahla
Powiązania:: https://bibliotekanauki.pl/articles/31342281.pdf
Data publikacji:: 2018-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: domination
reconfiguration
Opis:: We consider γ-graphs, which are reconfiguration graphs of the minimum dominating sets of a graph G. We answer three open questions about γ-graphs of trees by providing upper bounds on the maximum degree, the diameter, and the number of minimum dominating sets. The latter gives an upper bound on the order of the γ-graph.
Źródło:: Discussiones Mathematicae Graph Theory; 2018, 38, 3; 703-716
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 5.

Tytuł:: Oriented Incidence Colourings of Digraphs
Autorzy:: Duffy, Christopher
MacGillivray, Gary
Ochem, Pascal
Raspaud, André
Powiązania:: https://bibliotekanauki.pl/articles/31343581.pdf
Data publikacji:: 2019-02-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: digraph homomorpism
graph colouring
incidence colouring
computational complexity
Opis:: Brualdi and Quinn Massey [6] defined incidence colouring while studying the strong edge chromatic index of bipartite graphs. Here we introduce a similar concept for digraphs and define the oriented incidence chromatic number. Using digraph homomorphisms, we show that the oriented incidence chromatic number of a digraph is closely related to the chromatic number of the underlying simple graph. This motivates our study of the oriented incidence chromatic number of symmetric complete digraphs. We give upper and lower bounds for the oriented incidence chromatic number of these graphs, as well as digraphs arising from common graph constructions and decompositions. Additionally we construct, for all k > 2, a target digraph H_k for which oriented incidence k colouring is equivalent to homomorphism to H_k.
Źródło:: Discussiones Mathematicae Graph Theory; 2019, 39, 1; 191-210
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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