Regular Graphs of given Girth

Graph theory is the study of mathematical structures called graphs. We define a graph as a pair (V,E), where V is a nonempty set, and E is a set of unordered pairs of elements of V . V is called the set of vertices of G, and E is the set of edges. Two vertices a and b are adjacent provided (a, b) ∈ E. If a pair of vertices is adjacent, the vertices are referred to as neighbors. We can represent a graph by representing the vertices as points and the edges as line segments connecting two vertices, where vertices a, b ∈ V are connected by a line segment if and only if (a, b) ∈ E. Figure 1 is an example of a graph with vertices V = {x, y, z, w} and edges E = {(x,w), (z, w), (y, z)}.