2011•Journal of Scientific ResearchOpen access

Complete Cototal Domination Number of a Graph

B. Basavanagoud, Sunilkumar M. Hosamani

Abstract

Let be a graph. A set of a graph is called a total dominating set if the induced subgraph has no isolated vertices. The total domination number of G is the minimum cardinality of a total dominating set of G. A total dominating set D is said to be a complete cototal dominating set if the induced subgraph has no isolated vertices. The complete cototal domination number of G is the minimum cardinality of a complete cototal dominating set of G. In this paper, we initiate the study of complete cototal domination in graphs and present bounds and some exact values for . Also its relationship with other domination parameters are established and related two open problems are explored.Keywords: Domination number; Total domination number; Cototal domination number; Complete cototal domination number.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i3.7744 J. Sci. Res. 3 (3), 557-565 (2011)

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Key concepts: Dominating set, Domination analysis, Combinatorics, Mathematics, Induced subgraph, Graph, Cardinality (data modeling), Set (abstract data type)