Independent point-set domination in line graphs

Abstract

Line graph of a graph G is an intersection graph of the edge set E(G) of G. In this paper, we obtain a sharp upper bound on the diameter of graph G whose line graph is an ipsd graph (graph possessing an independent point-set dominating set) by establishing a fundamental relation between diameter of G and diameter of its line graph L(G). We prove that if for a graph G, the length of the longest induced cycle is greater than 5, then its line graph does not possess an ipsd-set. Further we characterize certain classes of graphs viz., trees, complete graphs and complete bipartite graphs whose line graphs possess an independent point set dominating set.