摘要：The modified first Zagreb connection index ZC 1 ∗ is a graph invariant that appeared about fifty years ago within a study of molecular modeling, and after a long time, it has been revisited in two papers ((Ali and Trinajstić, 2018) and (Naji et al., 2017)) independently. For a graph G , this graph invariant is defined as ZC 1 ∗ G = ∑ v ∈ V G d v τ v , where d v is the degree of the vertex v and τ v is the connection number of v (that is, the number of vertices having distance 2 from v ). In this paper, the graphs with maximum/minimum ZC 1 ∗ value are characterized from the class of all n -vertex trees with fixed number of pendent vertices (that are the vertices of degree 1).
