Note on the unicyclic graphs with the first three largest Wiener indices

Abstract

© 2018 University of Kragujevac, Faculty of Science. Let G = (V,E) be a simple connected graph with vertex set V and edge set E. Wiener index W(G) of a graph G is the sum of distances between all pairs of vertices in G, i.e., W(G) = σ[u,v]⊆G dG(u, v), where dG(u, v) is the distance between vertices u and v. In this note we give more precisely the unicyclic graphs with the first tree largest Wiener indices, that is, we found another class of graphs with the second largest Wiener index.