Decomposition of Complete Multigraph into Wheel Graphs for Cyclic Triple System-Reference-Cited by-同舟云学术

Decomposition of Complete Multigraph into Wheel Graphs for Cyclic Triple System

Published:2023-12-28 Issue: Volume:22 Page:950-960
ISSN:2224-2880
Container-title:WSEAS TRANSACTIONS ON MATHEMATICS
language:en
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Author:

Matarneh Khaled Ahmad¹,Al-Qadri Mowafaq Omar²,Al-Husban Abdallah³,Aldiabat Raja'i⁴,Alshorm Shameseddin⁵

Affiliation:

1. Faculty of Computer Studies, Arab Open University (AOU), Riyadh, KINGDOM OF SAUDI ARABIA

2. Department of Mathematics, Jerash University, Jerash, JORDAN

3. Department of Mathematics, Faculty of Science and Technology, Irbid National University, JORDAN

4. Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, KINGDOM OF SAUDI ARABIA

5. Department of Mathematics, Al Zaytoonah, University of Jordan, Amman 11733, JORDAN

Abstract

Let 𝑛 be positive integer and 𝑊𝑛 be a wheel graph of order 𝑛. In this paper, we construct a new decomposition of 8𝐾𝑣 into wheel graphs for 𝑣 ≡ 2 (mod 12). Then, new cyclic triple system will be defined to arrange 𝑣 × 2(𝑣 − 1) triples satisfying certain criteria. In this development, the decomposition of 8𝐾𝑣 will be used to construct a cyclic 12-fold triple system of order 𝑣 ≡ 2 (mod 12).

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Subject

General Mathematics

Reference21 articles.

1. R. M. Wilson, “Decompositions of complete graphs into subgraphs isomorphic to a given graph,” in Proc. 5th British Combinatorial Conf., 1975.

2. Z. Liang and J. Guo, “Decomposition of complete multigraphs into crown graphs,” Journal of Applied Mathematics and Computing, vol. 32, pp. 507-517, 2010.

3. M. Tarsi,” Decomposition of a complete multigraph into simple paths: non balanced handcuffed designs,” Journal of Combinatorial Theory, Series A, vol. 34, pp. 60-70, 1983.

4. V. Chitra and A. Muthusamy, “Symmetric Hamilton cycle decompositions of complete multigraphs,” Discussiones Mathematicae Graph Theory, vol. 33, pp. 695-707, 2013.

5. Z. Tian and R. Wei, “Decomposing triples into cyclic designs,” Discrete Mathematics, vol. 310, pp. 700-713, 2010.