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Strong and weak domination in graphs

✍ Scribed by V. Swaminathan; P. Thangaraju


Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
168 KB
Volume
15
Category
Article
ISSN
1571-0653

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πŸ“œ SIMILAR VOLUMES


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This paper generalizes dominating and efficient dominating sets of a graph. Let G be a graph with vertex set V(G). If f: V(G) ~ Y, where Y is a subset of the reals, the weight off is the sum of f(v) over all ve V(G). If the closed neighborhood sum off(v) at every vertex is at least 1, thenfis called

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In a graph G Γ… (V, E) if we think of each vertex s as the possible location for a guard capable of protecting each vertex in its closed neighborhood N[s], then ''domination'' requires every vertex to be protected. Thus, S ʚ V (G) is a dominating set if ʜ s √ S N[s] Γ… V (G). For total domination, eac

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## Abstract Let __G__ = (__V, E__) be a connected graph. A set __D__ βŠ‚ __V__ is a __set‐dominating set__ (sd‐set) if for every set __T__ βŠ‚ __V__ βˆ’ __D__, there exists a nonempty set __S__ βŠ‚ __D__ such that the subgraph γ€ˆ__S__ βˆͺ __T__〉 induced by __S__ βˆͺ __T__ is connected. The set‐domination number

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