Dacey Graphs

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].