Taichi Kousaka
Published 2017-10-05Version 1
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.
There does not exist a distance-regular graph with intersection array $\{80, 54,12; 1, 6, 60\}$
On almost distance-regular graphs
Distance-regular graphs with a few $q$-distance eigenvalues
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