Factorizations of the product of cycles

An -factorization of a graph is a partition of the edge set of into spanning subgraphs (or factors) each of whose components are isomorphic to a graph Let be the Cartesian product of the cycles with for each El-Zanati and Eynden proved that has a -factorization, where is a cycle of length if and onl...

Full description

Bibliographic Details
Main Authors: Y.M. Borse, A.V. Sonawane, S.R. Shaikh
Format: Article
Language:English
Published: Taylor & Francis Group 2019-12-01
Series:AKCE International Journal of Graphs and Combinatorics
Subjects:
Online Access:http://dx.doi.org/10.1016/j.akcej.2018.06.003
Description
Summary:An -factorization of a graph is a partition of the edge set of into spanning subgraphs (or factors) each of whose components are isomorphic to a graph Let be the Cartesian product of the cycles with for each El-Zanati and Eynden proved that has a -factorization, where is a cycle of length if and only if with We extend this result to get factorizations of into -regular, -connected and bipancyclic subgraphs. We prove that for the graph has an -factorization, where is an -regular, -connected and bipancyclic graph on vertices, if and only if divides and with
ISSN:0972-8600