On deriving explicit formulas of the surface areas for the arrangement graphs and some of the related graphs

Authors:
Eddie Cheng;Ke Qiu;Zhizhang Shen
Affiliations:
Department of Mathematics and Statistics, Oakland University, Rochester, MI, USA;Department of Computer Science, Brock University, St. Catharines, Ontario, Canada;Department of Computer Science and Technology, Plymouth State University, Plymouth, NH, USA
Venue:
International Journal of Computer Mathematics
Year:
2010

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Abstract

We derive an explicit formula for the surface area of the arrangement graph, i.e. the number of vertices at a certain distance from the identity vertex in such a graph. We also present such formulas for the star graph, the alternating group graph, and the split-star graph, via their respective structural relationship to the arrangement graph.