Toughness and (a,b,k)(a,b,k)-critical graphs

Let a,b,ka,b,k be nonnegative integers with 2⩽a

Research highlights
► We give some relations between toughness and (a,b,k)(a,b,k)-critical graphs.
► We obtain a result on (a,b,k)(a,b,k)-critical graphs depending on toughness and minimum degree.
► We show the main result in this paper is best possible in some sense.