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On minimal n-universal graphs

Published online by Cambridge University Press:  18 May 2009

J. W. Moon
J. W. Moon
Affiliation:
University College, London
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A graph Gn consists of n distinct vertices x1x2, …, xn some pairs of which are joined by an edge. We stipulate that at most one edge joins any two vertices and that no edge joins a vertex to itself. If xi, and xj are joined by an edge, we denote this by writing xi ∘ xj.

Consider a second graph HN, where n ≦ N. Following Rado [1], we say that a one-to-one mapping/of the vertices of Gn into the vertices of HN defines an embedding if xi ∘ xj implies f(xi) ∘ f(xj), and conversely, for all i, j = 1, 2,…, n. If there exists an embedding of Gn into HN, we denote this by writing Gn <HN. The particular graph HN is said to be n-universal if Gn < HN for every graph Gn with n vertices.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 7 , Issue 1 , January 1965 , pp. 32 - 33
Copyright
Copyright © Glasgow Mathematical Journal Trust 1965

References

1.Rado, R., Universal graphs, Ada Arith. (to appear).Google Scholar