On the Aα-spectral Radius of Graphs Without Large Matchings

作者：Hao, Yifang; Li, Shuchao^*; Zhao, Qin

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2022, 45(6): 3131-3156.

DOI：10.1007/s40840-022-01363-4

• A alpha-matrix
• A alpha-spectral radius
• Matching number
• Quotient matrix

Let G be an n-vertex graph. A matching in G is a set of independent edges, i.e., no two edges in the set are adjacent in G. The matching number is the maximal size of a matching in G. Nikiforov (Appl Anal Discrete Math 11(1):81-107, 2017) proposed the A(alpha)-matrix of a graph G, as follows: @@@ A(alpha)(G) = aD(G) + (1 - alpha) A(G), a epsilon [0, 1], @@@ where D(G) and A(G) are the diagonal degree matrix and adjacency matrix of G, respectively. In this contribution, we establish some A(alpha)-spectral conditions to guarantee that there do not exist large matchings in a graph G, recovering the previous results and obtaining similar results for a wide variety of spectral conditions from the A(alpha)-matrix. Our main tools are the Berge-Tutte formula and the double leading eigenvectors.