Subset powers of directed cycles

TL;DR

This paper investigates the structure of subset powers of directed cycles, specifically characterizing the cycle structure of the subset power of a directed cycle graph, which has implications for understanding complex graph transformations.

Contribution

It provides a complete characterization of the cycle structure of the subset power of directed cycles, a novel analysis in graph theory.

Findings

Determined the cycle structure of C^(d) for directed cycle C of length l.

Established conditions for the existence of certain cycles in subset powers.

Enhanced understanding of graph transformations and their cycle properties.

Abstract

For any directed graph G with vertex set V, the graph G^(d) is said to be a subset power of G and is defined to have vertex set equal to the set of d-element subsets of V; in G^(d), there is an edge from A to B if and only if we can label the elements of A and B such that there is an edge in G between each pair of corresponding elements. We determine the complete cycle structure of C^(d), where C is a directed cycle of length l.