Decompositions of some classes of regular graphs into cycles and paths of length eight

TL;DR

This paper investigates the conditions under which certain regular graphs, specifically tensor and wreath products of complete graphs, can be decomposed into cycles and paths of length eight.

Contribution

It provides necessary and sufficient conditions for the existence of (8; p, q)-decompositions in these classes of regular graphs.

Findings

Established conditions for tensor product decompositions.

Established conditions for wreath product decompositions.

Contributed to the understanding of cycle and path decompositions in regular graphs.

Abstract

Let $C_{k}$ (resp. $P_{k}$) denote the cycle (resp. path) of length $k$. In this paper, we examine the necessary and sufficient conditions for the existence of a $(8; p, q)$-decomposition of tensor product and wreath product of complete graphs.