On Highly-regular graphs

2017/10/05 by Taichi Kousaka, Kousaka, Taichi
Computer Science · Mathematics · #05C50 #05E30 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1710.01917

openalex publication_date 2017/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the Sims Conjecture and Distance Transitive Graphs

Related

• Edge-distance-regular graphs are distance-regular
• Distance-regular graph with large a1 or c2
• There exists no distance-regular graph with intersection array\n 56,36,9;1,3,48
• Some Spectral and Quasi-Spectral Characterizations of Distance-Regular Graphs
• A relationship between the diameter and the intersection number c2 for a distance-regular graph