# Applied Mathematics & Information Sciences

## 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.
6, Article 12.

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

Available at:
https://digitalcommons.aaru.edu.jo/amis/vol16/iss6/12