1974/12/01 by David P. Sumner · 58 citations
Computer Science · Mathematics · #Advanced Graph Theory Research #Graph Labeling and Dimension Problems #Graph theory and applications #Combinatorics #Vertex (graph theory) #Mathematics #Induced subgraph #Graph #Cardinality (data modeling) #Discrete mathematics #Undirected graph #Computer science
paper · pdf · doi:10.1017/s1446788700029232
published in Journal of the Australian Mathematical Society 18(4), 492-502 (Cambridge University Press)
openalex publication_date 1974/12/01 · openalex created_date 2022/05/12 · openalex updated_date 2026/08/04
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].