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

作者：Lei, Xingyu^*; Li, Shuchao; Wang, Jianfeng

来源：Bulletin of the Korean Mathematical Society, 2023, 60(4): 873-893.

DOI：10.4134/BKMS.b220340

• A(& alpha
• )-matrix
• A(a)-spectral radius
• size
• matching number

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).

• 单位
  山东理工大学