The existence of even factors based on the $A_\alpha$-spectral radius of graphs

TL;DR

This paper establishes a lower bound on the $A_eta$-spectral radius of a connected graph to determine the existence of an even factor, linking spectral properties to graph factorization.

Contribution

It provides a new spectral condition involving the $A_eta$-spectral radius that guarantees the existence of an even factor in connected graphs.

Findings

Lower bound on $A_eta$-spectral radius for even factors

Connection between spectral radius and graph factors

Conditions for even factor existence based on spectral properties

Abstract

An even factor of $G$ is a spanning subgraph $F$ such that every vertex in $F$ has a nonzero even degree. Note that $\delta(G)\geq2$ is a trivial necessary condition for a graph to have an even factor, where $\delta(G)$ is the minimum degree of $G$. In this paper, for a connected graph $G$ with minimum degree $\delta$, we establish a lower bound on the $A_\alpha$-spectral radius of $G$ such that $G$ contains an even factor.