On extra connectivity and extra edge-connectivity of balanced hypercubes

Abstract Given a graph G and a non-negative integer h , the h - extra connectivity (or h - extra edge-connectivity , resp.) of G , denoted by κ h ( G ) (or λ h ( G ), resp.), is the minimum cardinality of a set of vertices (or edges, resp.) in G , if it exists, whose deletion disconnects G and leaves each remaining component with more than h vertices. In this paper, we obtain a tight upper bound of the h -extra connectivity and the h -extra edge-connectivity of n -dimensional balanced hypercubes BH n for n  ≥ 2 and h ≤ 2 n − 1 . As an application, we prove that κ 4 ( B H n ) = κ 5 ( B H n ) = 6 n − 8 and λ 3 ( B H n ) = 8 n − 8 , which improves the previously known results given by Yang (2012) and Lu (2017).