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The modified first Zagreb connection index ZC1∗ 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 ZC1∗G=∑v∈VGdvτv, where dv is the degree of the vertex v and τv 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 ZC1∗ value are characterized from the class of all n-vertex trees with fixed number of pendent vertices (that are the vertices of degree 1).

Extremum Modified First Zagreb Connection Index of n-Vertex Trees with Fixed Number of Pendent Vertices