On the classification and dispersability of circulant graphs with two jump lengths

TL;DR

This paper classifies circulant graphs with two jump lengths and fully determines their dispersability, providing a comprehensive understanding of their structural and connectivity properties.

Contribution

It offers a complete classification of certain circulant graphs and solves the dispersability problem for graphs with specific jump sets.

Findings

Classified circulant graphs with two jump lengths

Solved dispersability for graphs with jump set {1, k}

Enhanced understanding of circulant graph structure

Abstract

In this paper, we give the classification of circulant graphs $C(\mathbb{Z}_{n},S)$ with $|S|=2$ and completely solve the dispersability of circulant graphs $C(\mathbb{Z}_{n},\{1, k\})$.