Domination number of a bipartite semigraph when it is a cycle

Abstract

Semigraph is a generalization of graph, with two or more vertices on edges which allows multiplicity in every concept of graph when it comes to semigraph. When number of vertices on the edges are restricted to two the semigraph is a graph, so every graph is a semigraph. In this article we deal with the variety of bipartite semigraphs, namely bipartite, s-bipartite and e-bipartite and bounds for their domination number (adjacent domination number and end vertex adjacent domination number) in particular when the semigraph is a cycle and also about possible size of the bipartite sets when the bipartite semigraph is a cycle.