Edge Bipancyclicity of Wheel Networks

Interconnection networks are usually modeled as undirected graphs. Two fundamental classes of interconnection networks structures are paths and cycles, which have desirable properties such as simple structures and low degrees. Therefore, the research about embedding paths and cycles into an interconnection network is a crucial topic. Edge bipancyclicity is a significant class of the cycle embedding problem in interconnection networks. A bipartite graph [Formula: see text] is referred to as bipancyclic if, there exist any possible [Formula: see text]-cycles ([Formula: see text] and [Formula: see text]) in [Formula: see text]. A bipartite graph [Formula: see text] is referred to as edge bipancyclic (respectively, vertex bipancyclic) if, each edge [Formula: see text] (respectively, vertex [Formula: see text]) of [Formula: see text] lies on all possible [Formula: see text]-cycles, where [Formula: see text] and [Formula: see text] [Formula: see text]. The [Formula: see text] [Formula: see text]-dimensional wheel network, denoted by [Formula: see text], is an important class of Cayley graphs in interconnection networks. The authors prove that [Formula: see text] [Formula: see text] is edge bipancyclic.