Spectral radius conditions for fractional $[a,b]$-covered graphs

TL;DR

This paper establishes precise spectral radius criteria that determine when a graph is fractional $[a,b]$-covered, linking spectral graph theory with fractional factor properties.

Contribution

It introduces tight spectral radius conditions that characterize fractional $[a,b]$-covered graphs, advancing the understanding of spectral conditions for fractional factors.

Findings

Derived tight spectral radius bounds for fractional $[a,b]$-covered graphs

Connected spectral properties with fractional factor existence

Provided new spectral criteria for fractional graph coverage

Abstract

A graph $G$ is called fractional $[a,b]$-covered if for every edge $e$ of $G$ there is a fractional $[a,b]$-factor with the indicator function $h$ such that $h(e)=1$. In this paper, we provide tight spectral radius conditions for graphs being fractional $[a,b]$-covered.