Weighted Peripheral Graph

Weighted peripheral graph Gd of a graph G has the peripheral vertices of G as its vertices and the diametral paths between the peripheral vertices of G as its edges. The structural properties of this weighted graph for some classes of graphs are discussed and bounds of certain parameters are identified. For the C# program developed to determine the parameters involved in the study, corresponding output for a sample graph is also presented. Remote nodes, high priority routes between them and strategic location problems of real life networks are some areas where these results can be applied.