On Orthogonal Special Class of Caterpillars Squares

Authors

R. El-Shanawany, Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf, EgyptFollow
E. El-Kholy, Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf, EgyptFollow
T. Homoda, Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf, EgyptFollow
Z. Bakr, Department of Mathematics, Faculty of Science, Tanta University, Tanta, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

Orthogonal Double Cover (ODC) is a set G of 2n subgraphs of a complete bipartite graph Kn,n of a graph G such that each edge in graph Kn,n appears once in both subgraphs of set G , and all subgraphs are isomorphic to graph G. we aim to construct two graph squares by a new engineering method that uses two induced starter functions to find the ODC of Kn,n. we also compose ODC from small to obtain a larger ODC. Starting from ODC F of Kq,q by qK2 we replace each point with n new points and each edge with the ODC of Kn,n to obtain the ODC of Kqn,qn by Some disjoint caterpillar unions, where q,n ∈ Z+.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/160612

Recommended Citation

El-Shanawany, R.; El-Kholy, E.; Homoda, T.; and Bakr, Z. (2022) "On Orthogonal Special Class of Caterpillars Squares," Applied Mathematics & Information Sciences: Vol. 16: Iss. 5, Article 12.
DOI: http://dx.doi.org/10.18576/amis/160612
Available at: https://digitalcommons.aaru.edu.jo/amis/vol16/iss5/12