Wiener index for graphs and their line graphs with arbitrary large cyclomatic numbers

AbstractThe Wiener number, W(G), is the sum of the distances of all pairs of vertices in a graph G. Infinite families of graphs with increasing cyclomatic number and the property W(G)=W(L(G)) are presented, where L(G) denotes the line graph of G. This gives a positive (partial) answer to an open question posed in an earlier paper by Gutman, Jovašević, and Dobrynin