Degree distance and Gutman index of increasing trees

Abstract

‎‎The Gutman index and degree distance of a connected graph G G are defined as‎ ‎‎‎Gut(G)=∑ {u,v}⊆V(G) d(u)d(v)d G (u,v)‎,‎ ‎‎Gut(G)=∑{u,v}⊆V(G)d(u)d(v)dG(u,v)‎,‎‎ ‎and‎ ‎‎‎DD(G)=∑ {u,v}⊆V(G) (d(u)+d(v))d G (u,v)‎,‎ ‎‎DD(G)=∑{u,v}⊆V(G)(d(u)+d(v))dG(u,v)‎,‎‎ ‎respectively‎, ‎where‎ ‎d(u) d(u) is the degree of vertex u u and d G (u,v) dG(u,v) is the distance between vertices u u and v v‎. ‎In this paper‎, ‎through a recurrence equation for the Wiener index‎, ‎we study the first two‎ ‎moments of the Gutman index and degree distance of increasing‎ ‎trees‎.

Keywords

• ‎‎Increasing trees‎
• the Wiener index‎
• ‎the Gutman index‎
• ‎degree distance