A relationship between the diameter and the intersection number c2 for a distance-regular graph

TL;DR

This paper investigates the relationship between the intersection number c2 and the diameter in distance-regular graphs, providing tools to identify bipartite and antipodal structures based on these parameters.

Contribution

It introduces new methods to analyze how large c2 influences bipartiteness and antipodality in distance-regular graphs.

Findings

Large c2 implies bipartiteness in certain graphs

Small kD suggests the graph is antipodal

Provides tools for structural characterization

Abstract

In this paper we will look at the relationship between the intersection number c2 and its diameter for a distance-regular graph. And also, we give some tools to show that a distance-regular graph with large c2 is bipartite, and a tool to show that if kD is too small then the distance-regular graph has to be antipodal.