Fair Secure Dominating Set in the Corona of Graphs
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The concept of fair secure dominating sets is extended by characterizing the corona of two nontrivial connected graphs and some important results are given.Abstract:
In this paper, we extend the concept of fair secure dominating sets by characterizing the corona of two nontrivial connected graphs and give some important results.read more
Citations
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Book ChapterDOI
A Theory of Graphs
David Gries,Fred B. Schneider +1 more
TL;DR: The theory of graphs has broad and important applications, because so many things can be modeled by graphs, and various puzzles and games are solved easily if a little graph theory is applied.
Journal ArticleDOI
Secure convex dominating sets in corona of graphs
TL;DR: In this paper, the secure convex dominating sets in the corona of two connected graphs were characterized and the corresponding security convex domination numbers of these graphs were determined, respectively.
Journal ArticleDOI
Secure convex dominating sets in products of graphs
TL;DR: The secure convex dominating sets in the lexicographic and Cartesian products of two connected graphs are characterized and the corresponding secure conveX domination numbers of these graphs are determined.
References
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Book ChapterDOI
A Theory of Graphs
David Gries,Fred B. Schneider +1 more
TL;DR: The theory of graphs has broad and important applications, because so many things can be modeled by graphs, and various puzzles and games are solved easily if a little graph theory is applied.
Book
A First Course in Graph Theory
Gary Chartrand,Ping Zhang +1 more
TL;DR: This book provides a rigorous yet informal treatment of graph theory with an emphasis on computational aspects ofgraph theory and graph-theoretic algorithms.
Journal ArticleDOI
Fair domination in graphs
TL;DR: It is shown that if G is a connected graph of order n ≥ 3 with no isolated vertex, then fd ( G ) ≤ n − 2, and an infinite family of connected graphs achieving equality in this bound is constructed.
Journal ArticleDOI
Secure convex domination in a graph
TL;DR: In this paper, the authors give necessary and sufficient conditions for a subset S of the vertex set of a connected graph G to be a secure convex dominating set and some realization problems are given.
Journal ArticleDOI
On a variant of convex domination in a graph
TL;DR: In this paper, a convex dominating set S which is also convex is called a restrained dominating set of G, and the minimum cardinality of a constrained dominating set is called the restrained convex domination number of G. In this paper we investigate the concept and give some important results.