Signless Laplacian spectral conditions for even factors in graphs

TL;DR

This paper establishes spectral conditions based on the signless Laplacian for guaranteeing the existence of even factors in connected graphs of even order.

Contribution

It introduces a new spectral criterion involving the signless Laplacian spectral radius for the existence of even factors in graphs.

Findings

Provides a sufficient spectral condition for even factors

Connects spectral graph theory with factor existence criteria

Enhances understanding of graph structure via signless Laplacian

Abstract

A spanning subgraph $F$ of a graph $G$ is defined as an even factor of $G$, if the degree $d_F(v)=2k, k\in\mathbb{N}^+$ for every vertex $v\in V(G)$. This note establishes a sufficient condition to ensure that a connected graph $G$ of even order with the minimum degree $\delta$ contains an even factor based on the signless Laplacian spectral radius.