Abstract
The generalized k-connectivity κk(G) of a graph G, introduced by Hager in 1985, is a natural generalization of the concept of connectivity κ(G), which is just for k=2. Rongxia Hao et al. determined the generalized 4-connectivity of the total graphs of the complete equipartition bipartite graph and conjectured that κ4(T(Km,m+1))=2m−1 and κ4(T(Km,n))=2m for n>m+1 and m≥4 in [Appl. Math. Comput. 422 (2022)]. In this paper, we solved this conjecture.
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