Orthogonal Double Covers of Complete Bipartite Graphs by Paths and Cycles

Higazy, M.; Scapellato, Raffaele

doi:10.17654/aadmjan2015_009_020

Cited by 3 publications

(1 citation statement)

References 8 publications

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“…The existence of ODCs has been considered and generalized by many authors [27][28][29]. The importance of ODC problems stems from solving database optimization problems; for example, when we look for specific information in a very large database, it takes too much time to find that information [30].…”

Section: P Xmentioning

confidence: 99%

On Orthogonal Double Covers and Decompositions of Complete Bipartite Graphs by Caterpillar Graphs

et al. 2023

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Nowadays, graph theory is one of the most exciting fields of mathematics due to the tremendous developments in modern technology, where it is used in many important applications. The orthogonal double cover (ODC) is a branch of graph theory and is considered as a special class of graph decomposition. In this paper, we decompose the complete bipartite graphs Kx,x by caterpillar graphs using the method of ODCs. The article also deals with constructing the ODCs of Kx,x by general symmetric starter vectors of caterpillar graphs such as stars–caterpillar, the disjoint copies of cycles–caterpillars, complete bipartite caterpillar graphs, and the disjoint copies of caterpillar paths. We decompose the complete bipartite graph by the complete bipartite subgraphs and by the disjoint copies of complete bipartite subgraphs using general symmetric starter vectors. The advantage of some of these new results is that they enable us to decompose the giant networks into large groups of small networks with the comprehensive coverage of all parts of the giant network by using the disjoint copies of symmetric starter subgraphs. The use case of applying the described theory for various applications is considered.

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