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Spectral conditions for factor-criticality of graphs

Jin Cai, Bo Zhou

Abstract

A graph $G$ is $k$-factor-critical if $G-S$ has a perfect matching for any $k$-subset $S$ of the vertex set of $G$. In this paper, we investigate the factor-criticality of graphs with fixed minimum degree and provide sufficient conditions for such graphs to be $k$-factor-critical in terms of spectral radius and signless Laplacian spectral radius.

Spectral conditions for factor-criticality of graphs

Abstract

A graph is -factor-critical if has a perfect matching for any -subset of the vertex set of . In this paper, we investigate the factor-criticality of graphs with fixed minimum degree and provide sufficient conditions for such graphs to be -factor-critical in terms of spectral radius and signless Laplacian spectral radius.
Paper Structure (5 sections, 11 theorems, 34 equations)

This paper contains 5 sections, 11 theorems, 34 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Results
  4. Spectral radius
  5. Signless Laplacian spectral radius

Key Result

Theorem 1.1

Let $G\in \mathbb{G}(n,\delta)$, where $n\geq 4\delta+3$. Let $k$ be an integer in $[0,\delta)$ with $k\equiv n \pmod 2$. If $\rho(G)\geq\rho(K_\delta\vee ((\delta-k+1)K_1\cup K_{n-2\delta+k-1}))$, then $G$ is $k$-factor-critical unless $G\cong K_\delta\vee((\delta-k+1)K_1\cup K_{n-2\delta+k-1})$, w

Theorems & Definitions (18)

  • Theorem 1.1
  • Theorem 1.2
  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • Lemma 3.1
  • proof
  • ...and 8 more