Abstract
The topology of interconnection networks determines the performance of the networks. Linear arrays and rings are two of the most fundamental structures of the interconnection network topologies owing to their simple structures and low degree. Thus how to embed cycles and paths into interconnection networks is a crucial factor for the networks. The interconnection network considered in this paper is the bubble-sort star graph. The n-dimensional bubble-sort star graph BS n is a bipartite and (2n - 3)-regular graph of order n!. A bipartite graph G of order IV(G)I is edge-bipancyclic if each edge of G lies on a cycle of all even length l with 4 ≤ l ≤ |V(G)|. In this paper, we show that the n-dimensional bubble-sort star graph BSn is edge-bipancyclic for n ≥ 3 and for each even length l with 4 ≤ l ≤ n!, every edge of BSn lies on at least four different cycles of length l. Moreover, we also have that BSn is vertex-bipancyclic and bipancyclic for n ≥ 3.
Highlights
Network topology is a crucial factor for the interconnection networks since it determines the performance of the networks
Paths and cycles are popular interconnection networks owing to their simple structures and low degree
We have investigated the edge-bipancyclicity of the bubble-sort star graphs
Summary
Network topology is a crucial factor for the interconnection networks since it determines the performance of the networks. An interconnection network is usually represented by an undirected simple graph where vertices represent processors and edges represent links between processors. A bipartite graph G of order n is bipancyclic if it contains a cycle of every possible even length between 4 and n. 2-good-neighbor diagnosability) of BSn. This paper deals with the edge-bipancyclicity of bubblesort star graphs. We will show that n-dimensional bubble-sort star graph BSn is edge-bipancyclic, vertex-bipancyclic, and bipancyclic for n ≥ 3 and for each even length l with 4 ≤ l ≤ n!, every edge of BSn lies on at least four different cycles of length l
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