Domination in Semigraphs

S. S. Kamath, R. S. Bhat

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Let G = (V, X) be a semigraph. A set D ⊆ V is called adjacent dominating set (ad-set) if for every υ ∈ V - D there exists a u ∈ D such that u is adjacent to v. The adjacency domination number γa = γa(G) is the minimum cardinality of an ad-set of G. Let Ve be the set of all end vertices in G. A set D ⊆ Ve is called end vertex adjacent dominating set (ead-set) if (i) D is an ad-set and (ii) Every end vertex υ ∈ V - D is e-adjacent to some end vertex u ∈ D in G. The end vertex adjacency domination number γea = γea(G) is the minimum cardinality of an ead-set of G. A set D C V is called consecutive adjacent dominating set (cad-set) if for every υ ∈ V - D there exists a u ∈ D such that u is ca-adjacent to v in G. The consecutive adjacency domination number γca = γca(G) is the minimum cardinality of a cad set of G. The above domination parameters are determined for various semigraphs and a few bounds are obtained.

Original languageEnglish
Pages (from-to)106-111
Number of pages6
JournalElectronic Notes in Discrete Mathematics
Volume15
DOIs
Publication statusPublished - 01-05-2003

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

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