Gutman Index and Detour Gutman Index of Pseudo-Regular Graphs

Abstract EN

The Gutman index of a connected graph G is defined as Gut(G)=∑u≠vd(u)d(v)d(u,v), where d(u) and d(v) are the degree of the vertices u and v and d(u,v) is the distance between vertices u and v.

The Detour Gutman index of a connected graph G is defined as GutG=∑u≠vd(u)d(v)D(u,v), where D(u,v) is the longest distance between vertices u and v.

In this paper, the Gutman index and the Detour Gutman index of pseudo-regular graphs are determined.