Study about End Edge Domination in Sub Division of Graphs

Abstract

Let \(S(G)\) be the subdivision graph of a graph \(G=(V,E)\). 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 \(\gamma_e'(S(G))\) of \(S(G)\) is the minimum cardinality of an end edge dominating set of \(S(G)\). In this chapter, some bounds for \(\gamma_e'(S(G))\) were obtained and exact values of \(\gamma_e'(S(G))\)  for some standard graphs were also obtained. Its correlations with other dominating parameters were also discovered. In G, we also relate split and end edge domination numbers.