On the Surface Areas of the Alternating Group Graph and the Split-Star Graph

Abstract

An important invariant of an interconnection network is its surface area, the number of nodes at distance \(i\) from a node. We derive explicit formulas, via two different approaches: direct counting and generating function, for the surface areas of the alternating group graph and the split-star graph, two Cayley graphs that have been
proposed to interconnect processors in a parallel computer.