Algorithm for 2-Vertex Connectivity in Directed Graphs

Abstract

Graph theory is very important in solving many problems efficiently. Each graph is made up of vertices and edges. Common notation used to represent a graph is G = (V, E) where V is a set of vertices and E is a set of edges. The dynamics of graphs were understood and explored well in the literature while there is insufficient research related to directed graphs. There are many problems to be solved with respect to graphs. For instance, 2-vertex connectivity is an important problem to be addressed. Recently Georgiadis et al. focused on this problem and found that two vertices v and w are 2-vertex connected when there are two internally vertex -disjoint paths coming from v to w and two internally vertex disjoint paths from w to v. Many kinds of combinations were explored in their work. However, it is useful to have more investigation on this. In this paper we reviewed directed graphs with 2-vertex connectivity with some algorithms. Our study reviewed that the approaches can be used effectively to solve select problems in the real world.