(m, e)-domination in Semigraphs

N.S. Bhave and B.Y. Bam [S. S. Kamath and Saroja R. Hebbar, Strong and weak Domination, Full sets and Domintion Balance in Semigraphs, Preprint], introduced the concept of middle end degree ((m, e)− degree) of a vertex in a semigraph. This paper is devoted to a particular type of a-domination in which the (m, e)− degree plays a part. A vertex u (m, e)-strong dominates another vertex v if u and v are adjacent and d m e ( u ) ⩾ d m e ( v ) in the lexico graphic order. (m, e)- dominating sets and (m, e)- domination number are defined and studied in this paper.