On Edge Addition Problem with some graphs

Abstract

The two questions that: how many edges at least have to be added to the network to ensure the message within the effective bounds, and how large message delay will be increased when faults occur, can re-write this problem as: What the minimum diameter of a connected graph obtained from a graph of diameter after adding extra edges, this problem called "Edge Addition Problem". In this paper we find some exact values to above problem by using some special graphs (Line Graph, Bipartite graph, and complete Bipartite graph).