[1,2]-Complementary connected domination number of graphs-III

Abstract

A set S⊆V(G) in a graph G is said to be [1,2]-complementary connected dominating set if for every vertex v∈V-S, 1≤|N(v)∩S|≤2 and <V-S> is connected. The minimum cardinality of [1,2]-complementary connected dominating set is called [1,2]-complementary connected domination number and is denoted by γ_{[1,2]cc}(G). In this paper, we investigate 3-regular graphs on twelve vertices for which γ_{[1,2]cc}(G)=χ(G)=3.