Maxima of the Aα-Index of Non-Bipartite C3-Free Graphs for 1/2 < α < 1

In 2017, Nikiforov defined the A alpha-matrix of the graph G as A(alpha)(G)=alpha D(G)+(1-alpha)A(G),0 <=alpha <= 1, which merges the diagonal degree matrix D(G) and the adjacency matrix A(G). In this paper, we characterize the graphs which attain the maximum A(alpha)-index among triangle-free non-bipartite graphs of order n for 1/2<alpha<1.