Fair domination in graphs
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TLDR
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.About:
This article is published in Discrete Mathematics.The article was published on 2012-10-06 and is currently open access. It has received 50 citations till now. The article focuses on the topics: Bound graph & Graph power.read more
Citations
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[1, 2]-sets in graphs
TL;DR: This paper relates the concept of [j,k]-sets to a host of other concepts in domination theory, including perfect domination, efficient domination, nearly perfect sets, 2-packings, and k-dependent sets, and determines bounds on the cardinality of minimum [1, 2]-sets, and investigates extremal graphs achieving these bounds.
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Partial domination - the isolation number of a graph
Yair Caro,Adriana Hansberg +1 more
TL;DR: In this paper, it was shown that if G is a connected graph on n ≥ 6 vertices, then there exists a set of vertices D with D ≤ n/3 and such that V(G) n====== N[D] is an independent set.
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Fair Secure Domination in Graphs
TL;DR: In this paper, it was shown that given positive integers, and such that there exists a connected nontrivial graph with such that and the set is a dominating set, the minimum cardinality of a fair secure dominating set of denoted by is called the fair secure domination number.
Book ChapterDOI
An Annotated Glossary of Graph Theory Parameters, with Conjectures
TL;DR: A glossary of 300 parameters of graphs, together with their definitions, and references to the authors who introduced them, can be found in this article, along with some 70 conjectures related to these parameters, more than 26 new parameters and open problem areas.
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Partial Domination in Graphs
TL;DR: In this article, the authors introduced the concept of partial domination in graphs and studied different bounds on the partial domination number of a graph with respect to its order, maximum degree, domination number etc.
References
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Book
Fundamentals of domination in graphs
TL;DR: Bounds on the domination number domination, independence and irredundance efficiency, redundancy and the duals changing and unchanging domination conditions on the dominating set varieties of domination multiproperty and multiset parameters sums and products of parameters dominating functions frameworks for domination domination complexity and algorithms are presented.
Book
Theory of graphs
TL;DR: In this article, the axiom of choice of choice is used to define connectedness path problems in directed graphs and cyclic graphs, as well as Galois correspondences of connectedness paths.
Journal ArticleDOI
Domination‐balanced graphs
Charles Payan,Nguyen Huy Xuong +1 more
TL;DR: The purpose of this paper is to characterize these graphs, which are called domination balanced if its vertex set can be partitioned into β(G) subsets so that each subset is a smallest dominating set of the complement G of G.
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Maximum k-regular induced subgraphs
TL;DR: It is proved that finding a maximum cardinality k-regular induced subgraph is an NP-hard problem for any fixed value of k, and a convex quadratic upper bound on the size of a k- regular induced sub graph is proposed.