A graph that does not have any loops or parallel edges. A simple path from one vertex to another that does not contain a repated vertex. Spanning Tree A subgraph of G that contains every vertex of G and is a tree. A tree in which one vertex is distinguished from the others and is called the root. Two vertices that are both children of the same parent are called siblings .
G is a tree if it is circuit-free and connected.
The walk consisting of walking from a vertex v to itself. The 'dots' in a graph.