Independence number and connectivity for fractional (a, b, k)-critical covered graphs

¹ School of Science, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212100, P.R. China
² School of Mathematics and Information Sciences, Yantai University, Yantai, Shandong 264005, P.R. China

^* Corresponding author: zsz_cumt@163.com

Received: 30 April 2021
Accepted: 18 July 2022

Abstract

A graph G is a fractional (a, b, k)-critical covered graph if G − U is a fractional [a, b]-covered graph for every U ⊆ V(G) with |U| = k, which is first defined by (Zhou, Xu and Sun, Inf. Process. Lett. 152 (2019) 105838). Furthermore, they derived a degree condition for a graph to be a fractional (a, b, k)-critical covered graph. In this paper, we gain an independence number and connectivity condition for a graph to be a fractional (a, b, k)-critical covered graph and verify that G is a fractional (a, b, k)-critical covered graph if

k(G) ≥ max {2b(a+1)(b+1)+4bk+5/4b,(a+1)²𝛼(G)+4bk+5/4b}.