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

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