Decompositions of Complete Multigraphs into Cyclic Designs

Mowafaq Alqadri - Universiti Utara Malaysia, Sintok, Kedah, Malaysia
Haslinda Ibrahim - Universiti Utara Malaysia, Sintok, Kedah, Malaysia
Sharmila Karim - Universiti Utara Malaysia, Sintok, Kedah, Malaysia


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DOI: http://dx.doi.org/10.30630/joiv.4.2.349

Abstract


Let  and  be positive integer,  denote a complete multigraph. A decomposition of a graph  is a set of subgraphs of  whose edge sets partition the edge set of . The aim of this paper, is to decompose a complete multigraph  into cyclic -cycle system according to specified conditions. As the main consequence, construction of decomposition of  into cyclic Hamiltonian wheel system, where , is also given. The difference set method is used to construct the desired designs.


Keywords


Cyclic design; Hamiltonian cycle; Near four factor; Wheel graph.

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References


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