On the surface area of the (n,k)-star graph

Authors:
Zhizhang Shen;Ke Qiu;Eddie Cheng
Affiliations:
Department of Computer Science and Technology, Plymouth State University, Plymouth, NH 03264, USA;Department of Computer Science, Brock University, St. Catharines, Ontario, L2S 3A1, Canada;Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

We present an explicit formula for the surface area of the (n,k)-star graph, i.e., the number of nodes at a certain distance from the identity node in the graph, by identifying the unique cycle structures associated with the nodes in the graph, deriving a distance expression in terms of such structures between the identity node of the graph and any other node, and enumerating those cycle structures satisfying the distance restriction. The above surface area derivation process can also be applied to some of the other node symmetric interconnection structures defined on the symmetric group, when the aforementioned distance expression is available.