الدكتور موفق القادري

Let v and λ be positive integer, λKv denote a complete multigraph. A decomposition of a graph G is a set of subgraphs of G whose edge sets partition the edge set of G. In this article, difference set method is used to introduce a new design that is decomposed a complete multigraph into near Hamiltonian cycles. In course of developing this design, a combination between near-4-factor and a cyclic (v − 1)-cycle system of 4Kv, when v = 4n + 2, n > 2, will be constructed.

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Alqadri, M., & Ibrahim

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Journal: AIP Conference Proceedings

This article aims to present a novel method, namely wheel partition technique, for constructing a new cyclic ????????-fold triple system called cyclic triple factorization denoted by ????????????(????). We prove the existence of ????????????(????) for ???? = ???????????? + ????????. Then, an arrangement of ???? × ????(???? − ????) triples of ????????????(????) is developed using the idea of decomposition of wheel graph into triangles (triples). Moreover, the starter triples algorithms of ????????????(????) are formulated to generate all triples.

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Mowafaq Alqadri, Haslinda Ibrahim, Sharmila Karim

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Journal: IAENG International Journal of Applied Mathematics

A near-????-factor of a graph is a spanning subgraph in which exactly one isolated vertex and all other vertices of order . In this paper, we employ the near-four-factor concept and -cycle system to present a new method for constructing a cyclic -fold triple system. Firstly, we would like to propose a new type of cyclic triple system called cyclic triple near factorization, denoted by . Then, we prove the existence of along with an algorithm for starter triples of for when is even. Finally, we use the construction of to demonstrate the existence of -factorization of for and .

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Alqadri. M., Ibrahim. H

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Journal: Journal of Engineering and Applied Sciences

Let v, λ be positive integers, λKv denote a complete multigraph on v vertices in which each pair of distinct vertices joining with λ edges. In this article, difference method is used to introduce a new design that decomposes 4Kv into cycles, when v ≡ 2, 10(mod12). This design merging between cyclic ( ) m mr , ..., 1 -cycle system and near-fourfactor is called a near cyclic ( ) m mr , ..., 1 -cycle system

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Mowafaq Alqadri, Haslinda Ibrahim

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Journal: Far East Journal of Mathematical Sciences (FJMS)