Abstract
The modified first Zagreb connection indexZC1∗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 graphG, this graph invariant is defined asZC1∗G=∑v∈VGdvτv, wheredvis the degree of the vertexvandτvis the connection number ofv(that is, the number of vertices having distance 2 fromv). In this paper, the graphs with maximum/minimumZC1∗value are characterized from the class of alln-vertex trees with fixed number of pendent vertices (that are the vertices of degree 1).
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