Results 51 to 60 of about 1,497 (106)
A Constructive Characterization of Vertex Cover Roman Trees
Discussiones Mathematicae Graph Theory, 2021 A Roman dominating function on a graph G = (V (G), E(G)) is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex u for which f (u) = 0 is adjacent to at least one vertex v for which f (v) = 2.
Martínez Abel Cabrera +2 more
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Total Dominator Chromatic Number on Various Classes of Graphs
International journal of scientific research and reviews, 2019 Let G be a graph with minimum degree at least one. A total dominator coloring of G is a proper coloring of G with the extra property that every vertex in G properly dominates a color class.
Dr.A. Vijayalekshmi, S. Anusha
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Changing and Unchanging of the Domination Number of a Graph: Path Addition Numbers
Discussiones Mathematicae Graph Theory, 2021 Given a graph G =(V, E) and two its distinct vertices u and v, the (u, v)-Pk-addition graph of G is the graph Gu,v,k−2 obtained from disjoint union of G and a path Pk : x0, x1,...,xk−1, k ≥ 2, by identifying the vertices u and x0, and identifying the ...
Samodivkin Vladimir
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A NOTE ON THE HOP DOMINATION NUMBER OF A SUBDIVISION GRAPH
International Journal of Apllied Mathematics, 2019 Let G = (V,E) be a graph with p vertices and q edges. A subset S ⊂ V (G) is a hop dominating set of G if for every v ∈ V − S, there exists u ∈ S such that d(u, v) = 2. The minimum cardinality of a hop dominating set of G is called a hop domination number
C. Natarajan, S. Ayyaswamy
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On the Lovasz O-number of Almost Regular Graphs With Application to Erdos-Renyi Graphs [PDF]
AMS classifications: 05C69; 90C35; 90C22;Erdos-Renyi graph;stability number;Lovasz O-number;Schrijver O-number;C*-algebra;semidefinite ...
Klerk, E. de +3 more
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Connected domination game played on Cartesian products
Open Mathematics, 2019 The connected domination game on a graph G is played by Dominator and Staller according to the rules of the standard domination game with the additional requirement that at each stage of the game the selected vertices induce a connected subgraph of G. If
Bujtás Csilla +3 more
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On the number of outer connected dominating sets of graphs
, 2012 Let $G=(V,E)$ be a simple graph. A set $S\subseteq V(G)$ is called an outer-connected dominating set (or ocd-set) of $G$, if $S$ is a dominating set of $G$ and either $S=V(G)$ or $V\backslash S$ is a connected graph.
Akhbari, Mohammad H. +2 more
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Factor-Critical Property in 3-Dominating-Critical Graphs
, 2006 A vertex subset $S$ of a graph $G$ is a dominating set if every vertex of $G$ either belongs to $S$ or is adjacent to a vertex of $S$. The cardinality of a smallest dominating set is called the dominating number of $G$ and is denoted by $\gamma(G)$.
Wang, Tao, Yu, Qinglin
core
On Nordhaus-Gaddum type relations of δ-complement graphs. [PDF]
Heliyon, 2023 Vichitkunakorn P +2 more
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Power Domination in the Generalized Petersen Graphs
Discussiones Mathematicae Graph Theory, 2020 The problem of monitoring an electric power system by placing as few measurement devices in the system can be formulated as a power dominating set problem in graph theory.
Zhao Min, Shan Erfang, Kang Liying
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