Length two path centered surface areas of the (n, k)-star graph

We discuss the notion of H-centered surface area of a connected graph G, where H is a subgraph of G, i.e., the number of vertices in G at a certain distance from H, and focus on the special case when H is a length two path. In particular, we derive explicit formulas for the length two path centered surface areas of the edge-asymmetric (n, k)-star graph, centered on two kinds of length two paths, via a multivariate generating function approach.