The high order spectral extrema of $2K_r$-free graphs

TL;DR

This paper identifies extremal graphs with maximum clique spectral radii in $2K_r$-free graphs, extending Turán-type results to spectral graph theory for large $n$.

Contribution

It provides spectral extremal results for $2K_r$-free graphs, including maximum sum and 3-clique spectral radii, generalizing Turán number findings.

Findings

Identified graphs with maximum sum of clique spectral radii for $2K_r$-free graphs.

Determined the maximum 3-clique spectral radius among $2K_3$-free graphs.

Extended Turán number results to spectral graph theory context.

Abstract

In this paper, we determine the graphs with maximum value of the sum number from $k$-clique spectral radius to $(2r-1)$-clique spectral radius among all $2K_{r}$-free graphs on $n$ vertices for $ r\le k$ and large $n$. We also determine the graphs with maximum $3$-clique spectral radius among all $2K_{3}$-free graphs on $n$ vertices. Our results are spectral versions of some results on generalized Tur\'an numbers.