Gutman Index and Detour Gutman Index of Pseudo-Regular Graphs

摘要

The Gutman index of a connected graph G is defined as Gut(G) = Σ_(u≠v)d(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 Gut(G) = Σ_(u≠v)d(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.