End edge domination in sub division of graphs

Abstract

Let S(G) be the subdivision graph of a graph G. An edge dominating set D of a sub division graph S(G)  is an end edge dominating set if D contains all end edges of S(G). The end edge domination number of S(G) is the minimum cardinality of an end edge dominating set of S(G). In this paper, some bounds for end edge domination number in S(G) were obtained and exact values of for some graphs were also obtained. Further its relationships with other different domination parameters were obtained. Also we relate split domination and end edge domination numbers in G.