Abstract
An undirected graph is said to be edge-regular with parameters (υ,k,λ) if it consists of v vertices, the degree of each vertex is k, and each edge belongs to precisely A triangles. It is proved that every edge-regular graph with parameters (v, k, A) in which 3A ≤ 2k — 5 either has the diameter 2, or is a polygon or else the icosahedron, unless k = 4 and A = 1.
This research was supported by the Russian Foundation for Basic Research (Grant 94-01-00802-a) and the Foundation of the State Committee for Higher Education of the Russian Federation.
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References
A. E. Brouwer, A. M. Cohen, and A. Neumaier (1989) Distance-Regular Graphs, Springer-Verlag, Berlin etc.
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© 1997 Springer Science+Business Media Dordrecht
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Makhnëv, A.A. (1997). Regular Graphs Whose Every Edge Belongs to Many Triangles. In: Operations Research and Discrete Analysis. Mathematics and Its Applications, vol 391. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5678-3_13
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DOI: https://doi.org/10.1007/978-94-011-5678-3_13
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