Role of Incidence Metric With Special Reference to Its Relationship Between Two Classes of Objects: Exploring the relationship between connectivity and incidence metric in graphs

Abstract

In an undirectedgraph G, two vertices u and v arecalled connected if G contains a path from u to v.Otherwise, they are called disconnected.A graph is called connected ifevery pair of distinct vertices in the graph is connected; otherwise, it iscalled disconnected. A graph iscalled k-vertex-connected or k-edge-connected ifno set of k-1 vertices(respectively, edges) exists that, when removed, disconnects the graph. A k-vertex-connected graph is oftencalled simply k-connected. A directedgraph is called weaklyconnected if replacing all of its directed edges with undirectededges produces a connected (undirected) graph. It is strongly connected or strong if it contains a directedpath from u to v and a directed path from v to u for every pair ofvertices u, v.