Isolated toughness variant and fractional κ-factor

Isolated toughness is a crucial parameter considered in network security which characterizes the vulnerability of the network from the perspective of graph topology. I ’( G ) is the unique variant of isolated toughness which was introduced in 2001. This work investigates the correlation of I ’( G ) and the existence of fractional factor. It is proved that a graph G with δ ( G ) ≥ k admits fraction k -factor if I ’( G ) > 2 k − 1, where k ≥ 2 is an integer. A counterexample is presented to show the sharpness of I ’( G ) bound.