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arXiv · 1710.01917

On Highly-regular graphs

Taichi Kousaka
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Abstract

Highly-regular graphs can be regarded as a combinatorial generalization of distance-regular graphs. From this standpoint, we study combinatorial aspects of highly-regular graphs. As a result, we give the following three main results in this paper. Firstly, we give a characterization of a distance-regular graph by using the index and diameter of a highly-regular graph. Secondly, we give two constructions of highly-regular graphs. Finally, we generalize well-known properties of the intersection numbers of a distance-regular graph.

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Taichi Kousaka. 2017-10-05. On Highly-regular graphs. https://arxiv.org/abs/1710.01917

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