Computing the eccentric connectivity index and eccentric adjacency index of conjugated trees

Abstract

Let G be a connected graph with n vertices and m edges. The eccentricity of a vertex u 6 V(G), denoted by ec(u), is the maximum distance between u and any other vertex of G. The degree of a vertex u e V(G), denoted by dc(w), is the number of incident edges to u. The eccentric connectivity index of G is defined as £C(G) = dc(u)ec(u) and the eccentric adjacency index is de-V(G) fined as (G) = J2 where Sc(u) is the sum of degrees ueV(G) eGW of neighbors of the vertex u in G. In this paper, we determine the smallest and largest eccentric connectivity index of conjugated trees. Also, we find the extremal conjugated trees with respect to eccentric adjacency index. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.