A spectral extremal problem on graphs with given size and matching number

TL;DR

This paper investigates the maximum spectral radius of graphs with specified size and matching number, identifying extremal graphs and extending classical spectral extremal problems.

Contribution

It determines the maximal Q-spectral radius for graphs with given size and matching number, and characterizes the extremal graphs.

Findings

Maximal Q-spectral radius for graphs with given size and matching number identified

Extremal graphs characterized explicitly

Extends spectral extremal problem to matching number constraints

Abstract

Brualdi and Hoffman (1985) proposed the problem of determining the maximal spectral radius of graphs with given size. In this paper, we consider the Brualdi-Hoffman type problem of graphs with given matching number. The maximal $Q$-spectral radius of graphs with given size and matching number is obtained, and the corresponding extremal graphs are also determined.