Aa-SPECTRAL EXTREMA OF GRAPHS WITH GIVEN SIZE AND MATCHING NUMBER

摘要

In 2017, Nikiforov proposed the Aa-matrix of a graph G. This novel matrix is defined as A(a)(G) = aD(G) + (1- a)A(G), a ? [0, 1],where D(G) and A(G) are the degree diagonal matrix and adjacency matrix of G, respectively. Recently, Zhai, Xue and Liu [39] considered the Brualdi-Hoffman-type problem for Q-spectra of graphs with given matching number. As a continuance of it, in this contribution we consider the Brualdi-Hoffman-type problem for Aa-spectra of graphs with given matching number. We identify the graphs with given size and matching number having the largest A(a)-spectral radius for a ? [1/2, 1).

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