Dacey Graphs

Abstract

In this paper our graphs will be finite, undirected, and without loops or multiple edges. We will denote the set of vertices of a graph G by V(G). If G is a graph and u, v∈V(G), then we will write u ∼ v to denote that u and v are adjacent and u ≁ v otherwise. If A ⊆ V(G), then we let N(A) = {u∈ V(G)|u ∼ a for each a ∈A}. However we write N(v) instead of N({v}). When there is no chance of confusion, we will not distinguish between a subset A ⊆ V(G) of vertices of G and the subgraph that it induces. We will denote the cardinality of a set A by |A|. The degree of a vertex v is δ(v) = |N(v)|. Any undefined terminology in this paper will generally conform with Behzad and Chartrand [1].