The g-Extra Mixed Connectivity of Hypercube-Like Networks

The [Formula: see text]-extra (edge) connectivity, proposed by Fàbrega and Fiol [7, 8], is a generalization of traditional (edge) connectivity and assumes that only vertices (resp. edges) may be faulty. This paper considers [Formula: see text]-extra mixed connectivity proposed by Wang and Wang [19] because vertices and edges of a network may fail simultaneously in reality. Then, we acquire a lower bound to the [Formula: see text]-extra mixed connectivity of hypercube-like networks when [Formula: see text]. Moreover, we show that the suggested bound is sharp by providing the [Formula: see text]-extra mixed connectivity for some hypercube-like networks, including hypercubes, bicubes, locally twisted cubes, Möbius cubes, and twisted cubes.