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

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