Secure Node Covering of Cocktail Party Graphs and Generalized Fan Graphs

Abstract

Combinatorial problems have become more important recently in the study of coverage, connectivity, and fault tolerance in communication networks. A communication network's topology is often modelled as an undirected graph G = (V, E) in which the set of vertices V and the set of edges E correspond to nodes and links of the network respectively. The key idea behind the notion of vertex covering is to minimize the number of nodes with the property that, all the communication links in the network are secure. To achieve this operation, nodes in the minimum vertex cover set are trusted and can monitor transmission between nodes, since every communication link will be under the coverage of one or more nodes. This paper analyses the vertex and edge covers of Cocktail Party and Generalized Fan Graphs.