Tight Toughness and Isolated Toughness for \K₂, Cₙ\-factor critical avoidable graph

A spannning subgraph F of G is a \K₂, Cₙ\-factor if each component of F is either K₂ or C₍. A graph G is called a (\K₂, Cₙ\, n) -factor critical avoidable graph if G-X-e has a \K₂, Cₙ\-factor for any S V (G) with |X|=n and e E (G-X). In this paper, we first obtain a sufficient condition with regard to isolated toughness of a graph G such that G is \K₂, C₍\-factor critical avoidable. In addition, we give a sufficient condition with regard to tight toughness and isolated toughness of a graph G such that G is \K₂, C₂₈+₁|i 2\-factor critical avoidable respectively.