Constructing Dominating Sets in Circulant Graphs

TL;DR

This paper presents an efficient method to construct small dominating sets in circulant graphs using bounds on double exponential sums, advancing understanding of graph domination in this class.

Contribution

It introduces a new construction technique for dominating sets in circulant graphs based on exponential sum bounds, improving previous approaches.

Findings

Constructed small dominating sets efficiently.

Established bounds on double exponential sums.

Enhanced understanding of domination in circulant graphs.

Abstract

We give an efficient construction of a reasonably small dominating set in a circulant graph on $n$ notes and $k$ distinct chord lengths. This result is based on bounds on some double exponential sums. .