Dominating sets on the rhomboidal cactus chains andthe icosahedral network

Abstract

In this paper, we deal with the dominating set and the domination number of rhomboidal cactus chains. We determine minimum dominating sets and domination numbers of two special types of rhomboidal cactus chains, meta and ortho-chains. Thereafter, we determined the minimum dominating set for the icosahedral hexagonal network. Keywords: dominating set; rhomboidal cactus chains; icosahedral hexagonal network.