期刊论文

Li, Shuchao

英文

Discrete Applied Mathematics

0166-218X

2020

287

97-109

10.1016/j.dam.2020.08.004

Financially supported by the National Natural Science Foundation of China (Grant No. 11671164 ), and the Graduate Education Innovation Grant from Central China Normal University (Grant No. 2019CXPY001 ), and the Undergraduate Innovation and Entrepreneurship Grant from Central China Normal University (Grant No. CCNU202010511150 ).

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Let G be a graph, whose adjacency matrix and degree diagonal matrix are denoted by A(G) and D(G), respectively. In 2017 Nikiforov (2017) merged the A- and Q-spectral theories to proposed the Aα matrix: Aα(G)=αD(G)+(1−α)A(G), α∈[0,1]. Its largest eigenvalue is called the Aα-index of G. In this paper, we focus on specifying the property of the Aα matrix. On the one hand, we show that among the set of connected bipartite graphs of fixed order and size, the extremal graphs with the maximum Aα-index are the double nested graphs, i.e., bipa...