Abstract
Inequalities are obtained between the various parameters of a distance-regular graph. In particular, if k1 is the valency and k2 is the number of vertices at distance two from a given vertex, then in general k1 ⩽ k2. For distance-regular graphs of diameter at least four, k1=k2 if and only if the graph is simply a circuit. However when the diameter is two or three there are distance-regular graphs other than circuits for which k1=k2.
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© 1978 Springer-Verlag
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Taylor, D.E., Levingston, R. (1978). Distance-regular graphs. In: Holton, D.A., Seberry, J. (eds) Combinatorial Mathematics. Lecture Notes in Mathematics, vol 686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062547
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DOI: https://doi.org/10.1007/BFb0062547
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