A note on <i>g</i>-extra connectivity of hypercube-like networks

This research is supported by the National College Students' Innovation and Entrepreneurship Training Program (S202410530093), the National Natural Science Foundation of China(12301453), the Project of Education Department of Hunan Province(22B0180, 23B0125), the Project of Hunan Provincial Natural Science Foundation of China (2021JJ40522), the Project of Scientific Research Fund of Hunan Provincial Science and Technology Department (No. 2018WK4006), the 111 Project (No. D23017).<i>g</i>-extra connectivity of a connected graph <i>G</i>, denoted by κg(G), is a generalization of classical connectivity which related to the integer <i>g</i>. In this paper, we first construct a novel network named semicrossing cube SCQn. We prove that κ4(SCQn)=5n−13. This gives an answer to a problem proposed by Zhou (J. Comput. System Sci., 88(2017) 208-219).