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.