An odd [1, b]-factor in a graph from signless Laplacian spectral radius

School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212100, P.R. China

^* Corresponding author: zhousizhong@just.edu.cn

Received: 25 July 2023
Accepted: 6 December 2024

Abstract

An odd [1, b]-factor of a graph G is a spanning subgraph F of G such that d_F (u) is odd and 1 ≤ d_F (u) ≤ b for every u ∈ V (G), where b is a positive odd integer. The matrix Q(G) = D(G) + A(G) is called the signless Laplacian matrix of G, where D(G) denotes the degree diagonal matrix of G and A(G) denotes the adjacency matrix of G. Let q₁(G) denote the signless Laplacian spectral radius of G. In this paper, we study the existence of an odd [1, b]-factor of a graph G and derive a signless Laplacian spectral radius condition for a graph to possess an odd [1, b]-factor.