Abstract
The Aα-matrix of a graph G was defined by Nikiforov in 2017 as Aα(G)=αD(G)+(1−α)A(G), where α∈[0,1], D(G) and A(G) are the diagonal matrix of degrees and the adjacency matrix respectively. The largest eigenvalue of Aα(G) is called Aα-index of G. In this paper, we completely determine the extremal graphs with maximal Aα-index among all graphs with size m , domination number γ and no isolated vertices for α∈[12,1).
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