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Extremal graphs for inequalities involving domination parameters

✍ Scribed by Xu Baogen; E.J. Cockayne; Teresa W. Haynes; Stephen T. Hedetniemi; Zhou Shangchao

Book ID
108316413
Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
109 KB
Volume
216
Category
Article
ISSN
0012-365X

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A node in a graph G = (V,E) is said to dominate itself and all nodes adjacent to it. A set S C V is a dominating set for G if each node in V is dominated by some node in S and is a double dominating set for G if each node in V is dominated by at least two nodes in S. First we give a brief survey of

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We consider the well-known upper bounds Β΅(G) ≀ |V (G)|-βˆ†(G), where βˆ†(G) denotes the maximum degree of G and Β΅(G) the irredundance, domination or independent domination numbers of G and give necessary and sufficient conditions for equality to hold in each case. We also describe specific classes of gr