On bipartite distance-regular Cayley graphs with diameter $3$

TL;DR

This paper characterizes bipartite distance-regular Cayley graphs with diameter 3, showing they can generally be constructed from a semidirect product of a group and Z2, with one potential exception.

Contribution

It provides a classification of such graphs, revealing their construction method and identifying a possible unique case.

Findings

Most bipartite distance-regular Cayley graphs with diameter 3 are constructed from a semidirect product of a group and Z2.

The paper identifies a potential exception to this construction.

The classification advances understanding of the structure of these graphs.

Abstract

In this paper, we show that every bipartite distance-regular Cayley graph with diameter $3$ can be constructed on the semidirect product of a group and $\mathbb{Z}_{2}$, except possibly for one case.

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