For a family of connected graphs Formula: see text, an Formula: see text-factor is a spanning subgraph of a graph, whose connected components are isomorphic to graphs from the set Formula: see text. A graph Formula: see text is called an Formula: see text-factor avoidable graph if for any Formula: see text, Formula: see text admits an Formula: see text-factor excluding Formula: see text. Furthermore, a graph Formula: see text is called an Formula: see text-factor critical avoidable graph if for every Formula: see text with Formula: see text is an Formula: see text-factor avoidable graph. Let Formula: see text be a positive integer with Formula: see text, and write Formula: see text and Formula: see text, where Formula: see text and Formula: see text are two special families of trees. Some graph-based network parameters such as isolated toughness, binding number and degree sum, can directly measure the vulnerability of the network. In this paper, we use the these network parameters to study Formula: see text-factor critical avoidable graphs and Formula: see text-factor critical avoidable graphs, respectively.
Jin et al. (Fri,) studied this question.