Symmetric Property and Reliability of Balanced Hypercube

Two node-disjoint paths in balanced hypercubes

“…It is bipartite graph and node-transitive [16,26], but has smaller diameter than hypercubes and supports an efficient reconfiguration without changing the adjacent relationship among tasks [26]. In recent years, the balanced hypercube has attracted much attention in the literature [16,17,26,29,31,32].…”

Cyclic Vertex Connectivity of Trivalent Cayley Graphs

“…The cyclic vertex connectivity κ c (G) (cyclic edge connectivity λ c (G)) is defined as the minimum cardinality over all cyclic vertex-cut sets (cyclic edge-cut sets) of G if G has a cyclic vertex-cut set (cyclic edge-cut set). The cyclic vertex (cyclic edge) connectivity has been studied in [1]- [5], [7], [8], [10]- [14].…”

“…The cyclic vertex connectivity is an important measure for supporting the execution of parallel algorithms on cycles in a faulty and disconnected interconnection network. The cyclic vertex connectivity is determined for the following interconnection networks: star graphs [1], [11], bubble sort graphs [1], hierarchical cubic networks [2], complete cubic networks [3], and balanced hypercubes [14].…”

Automorphism group of the balanced hypercube

“…This often simplifies the computational and routing algorithms. It has been shown that the balanced hypercube is vertex-transitive and arc-transitive (see [14,22]). When dealing with the symmetry of graphs, the goal is to gain as much information as possible about the structure of the full automorphism groups.…”