Distance-regularised graphs are distance-regular or distance-biregular

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Abstract

One problem with the theory of distance-regular graphs is that it does not apply directly to the graphs of generalised polygons. In this paper we overcome this difficulty by introducing the class of distance-regularised graphs, a natural common generalisation. These graphs are shown to either be distance-regular or fall into a family of bipartite graphs called distance-biregular. This family includes the generalised polygons and other interesting graphs. Despite this increased generality we are also able to extend much of the basic theory of distance-regular graphs to our wider class of graphs. © 1987.

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Godsil, C. D., & Shawe-Taylor, J. (1987). Distance-regularised graphs are distance-regular or distance-biregular. Journal of Combinatorial Theory, Series B, 43(1), 14–24. https://doi.org/10.1016/0095-8956(87)90027-X

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