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- Title
On a combinatorial generalization of 27 lines associated with a cubic surface.
- Authors
Ahrens, R. W.; Szekeres, G.
- Abstract
Given integers 0 < λ < κ < ν, does there exist a nontrivial graph G with the following properties: G is of order ν (i.e. has ν vertices), is regular of degree κ (i.e. every vertex is adjacent to exactly κ other vertices), and every pair of vertices is adjacent to exactly λ others? Two vertices are said to be adjacent if they are connected by an edge. We call a graph with the above properties a symmetric (ν, κ, λ) graph and refer to the last of the properties as the A-condition. The complete graph of order v is a trivial example of a symmetric (ν, ν— 1, ν — 2) graph, but we are of course only interested in non-trivial constructions.
- Publication
Journal of the Australian Mathematical Society, 1969, Vol 10, Issue 3/4, p485
- ISSN
1446-7887
- Publication type
Article
- DOI
10.1017/S144678870000776X