Vertex edge connected from "summary" of Introduction to Graph Theory by Douglas Brent West
A graph is said to be vertex edge connected if for every pair of vertices in the graph, there is a path between them that contains at least one edge. In other words, a graph is vertex edge connected if it is possible to travel from any vertex to any other vertex by following a sequence of adjacent vertices connected by edges. This concept is important in understanding the connectivity of a graph and the relationships between its vertices and edges. Vertex edge connectivity is closely related to the concept of connectivity in graph theory. A graph is said to be connected if there is a path between every pair of vertices in the graph. Vertex edge connectivity takes this idea a step further by requiring that the path between two vertices contains at least one edge. This additional condition provides a more stringent measure of connectivity in a graph. To determine wheth...
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