ABSTRACT
A graphGwith n vertices andm edges consists of the vertex set V (G)={v1, v2, . . . , vn} and edge set E(G)={e1, e2, . . . , em}, where each edge consists of two (possibly equal) vertices called, endpoints. An element in V (G) is called a vertex of G. An element in E(G) is called an edge of G. Because graph theory has a variety of applications, we may also use a node for a vertex and a link for an edge to fit the common terminology in that area. We use the unordered pair (u, v) for an edge e={u, v}. If (u, v)∈E(G), then u and v are adjacent. We write u↔ v to mean u is adjacent to v. A loop is an edge whose endpoints are equal. Parallel edges or multiple edges are edges that have the same pair of endpoints. A simple graph is a graph having no loops or multiple edges. For a graph G= (V ,E), the underlying simple graph UG is the simple graph with vertex V and (x, y)∈E(UG) if and only if x = y and (x, y)∈E. A graph is finite if its vertex set and edge set are finite.We adopt the convention that every graph mentioned is finite.
