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Dacey Graphs

  • David P. Sumner (a1)
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 AV(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].

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[4] C. H. Randall and D. J. Foulis , ‘An approach to empirical logic’, Amer. Math. Monthly 77 (1970), 363374.

[8] D. P. Sumner , ‘Point determination in graphs’, Discrete Math. 5 (1973), 179187.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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