On sunlet graphs connected to a specific map on $\{1,2,\dots,p-1\}$

TL;DR

This paper investigates the structure of sunlet graphs derived from a specific map on the set of integers modulo an odd prime, revealing connections to the discrete logarithm problem.

Contribution

It introduces a novel analysis of sunlet graphs associated with a particular map on $oxed{1,2, ext{...},p-1}$, linking graph structure to number theory and cryptography.

Findings

Characterization of sunlet graph structures

Connection between graph walks and discrete logarithm problem

Insights into the algebraic properties of the map

Abstract

In this article, we study the structure of the graph implied by a given map on the set $S_p=\{1,2,\dots,p-1\}$, where $p$ is an odd prime. The consecutive applications of the map generate an integer sequence, or in graph theoretical context a walk, that is linked to the discrete logarithm problem.