科研之友
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摘要
In 2017, Nikiforov [12] proposed the A(alpha)-matrix of a graph G, which is defined as the convex linear combination of the adjacency matrix A(G) and the diagonal matrix of degrees D(G), i.e., A(alpha)(G) = alpha D(G) +(1-alpha)A(G), where alpha is an element of [0, 1]. In this paper, we determine the graph having the maximum A(alpha)- spectral radius for alpha is an element of [1/2, 1) among all connected graphs of size m and diameter (at least) d. As by-products, the extremal graphs with fixed size which attain the largest A(alpha)-spectral radius are characterized. Consequently the corresponding results for signless Laplacian matrix are deduced as well.
