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Total domination in block graphs

โœ Scribed by Gerard J Chang


Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
382 KB
Volume
8
Category
Article
ISSN
0167-6377

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## Abstract A set __S__ of vertices in a graph __G__ is a total dominating set of __G__ if every vertex of __G__ is adjacent to some vertex in __S__ (other than itself). The maximum cardinality of a minimal total dominating set of __G__ is the upper total domination number of __G__, denoted by ฮ“~__

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A set S of vertices of a graph G is a total dominating set, if every vertex of V (G) is adjacent to some vertex in S. The total domination number of G, denoted by ฮณ t (G), is the minimum cardinality of a total dominating set of G. We prove that, if G is a graph of order n with minimum degree at leas