On Some Bounds of Wiener Index of the Graphs with given Girth

Abstract

Let G be the simple connected graph with vertex set V(G) and edge set E(G). Wiener index
W(G) is a well-studied distance based index of a hydrogen suppressed molecular graph G which is defined
as the sum of distances between all pairs of vertices of G and the girth g of a graph G is a cycle which has
least number of edges among all the cycles in G. In this paper we arrive some bounds of Wiener index for
the graphs with given girth.