Distance-regular graphs

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Other literature type 01 Jan 1978Publisher:Springer Berlin Heidelberg

Authors: D. E. Taylor; Richard Levingston;

doi: 10.1007/bfb0062547

Distance-regular graphs

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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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University of Sydney
Australia

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