Abstract
The modified first Zagreb connection index ZC(1)* for a graph G is defined as ZC(1)*(G) = Sigma(v is an element of V(G)) d(v)tau(v), where d(v) is the degree of the vertex v and tau(v) is the connection number of v (that is, the number of vertices having distance 2 from v). A branching vertex of a graph is a vertex with degree greater than 2. In this paper, graphs with the maximum and minimum ZC(1)* values are characterized from the class of all trees of a fixed order and having a fixed number of branching vertices. (C) 2020 University of Kashan Press. All rights reserved