On Highly-regular graphs
Combinatorics
2017-10-06 v1
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.
Keywords
Cite
@article{arxiv.1710.01917,
title = {On Highly-regular graphs},
author = {Taichi Kousaka},
journal= {arXiv preprint arXiv:1710.01917},
year = {2017}
}