Extremal graphs for α- index

Abstract

Let N(G) be the number of vertices of the graph G. Let Pl(Bi) be the tree obtained of the path Pl and the trees B1, B2, ..., Bl by identifying the root vertex of Bi with the i-th vertex of Pl. Let Vm n = {Pl(Bi) : N(Pl(Bi)) = n;N(Bi) ≥ 2; l ≥ m}. In this paper, we determine the tree that has the largest α-index among all the trees in Vm n .