Edge Centered Surface Area for the \((n, k)\)-Star Graph

We suggest the notion of the surface area centered at an edge for a network structure, which generalizes the usual notion of surface area of a structure centered at a vertex. As a specific result, we derive explicit expressions of the edge-centered surface areas for the edge-asymmetric \((n, k)\)-star graph, following a generating function approach, in terms of two different kinds of edges.