| |
|
|
|
On Orthogonal Special Class of Caterpillars Squares |
|
|
|
PP: 953-959 |
|
|
|
doi:10.18576/amis/160612
|
|
|
|
Author(s) |
|
|
|
R. El-Shanawany,
E. El-Kholy,
T. Homoda,
Z. Bakr,
|
|
|
|
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+.
|
|
|
|
|
 |
|
