Wiener and Zagreb Indices for Line Graphs

The line graph \(L(G)\) of a connected graph G, has vertex set identical with the set of edges of \(G\), and two vertices of \(L(G)\) are adjacent if and only if the corresponding edges are adjacent in \(G\). Ivan Gutman et al examined the dependency of certain physio-chemical properties of alkanes in boiling point, molar volume, and molar refraction, heat of vapourization, critical temperature, critical pressure and surface tension on the Bertz indices of \(L'(G)\) Dobrynin and Melnikov conjectured that there exists no nontrivial tree \(T\) and \(i≥3\), such that \(W(L'(T)) = W(T)\). In this paper we study Wiener and Zagreb indices for line graphs of Complete graph, Complete bipartite graph and wheel graph.