On deriving explicit formulas of the surface areas for the arrangement graphs and some of the related graphs
Eddie Cheng, Ke Qiang Qiu, Zhizhang Shen · International Journal of Computer Mathematics · 2010
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.