On dispersability of some circulant graphs

TL;DR

This paper investigates the dispersability of certain circulant graphs by analyzing their matching book thickness and providing minimal page embeddings for specific classes, including bipartite and non-bipartite cases.

Contribution

It introduces new minimal page matching book embeddings for bipartite and non-bipartite circulant graphs within the Harary cube of a cycle and higher powers.

Findings

Matching book thickness equals maximum degree for studied graphs.

Minimal page embeddings are constructed for bipartite circulants.

Results extend to various higher powers of cycles.

Abstract

The matching book thickness of a graph is the least number of pages in a book embedding such that each page is a matching. A graph is dispersable if its matching book thickness equals its maximum degree. Minimum page matching book embeddings are given for bipartite and for most non-bipartite circulants contained in the (Harary) cube of a cycle and for various higher-powers.