"On Orthogonal Special Class of Caterpillars Squares" by R. El-Shanawany, E. El-Kholy et al.
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Applied Mathematics & Information Sciences

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

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