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k次Petersen连通圈网络
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Abstract:
互连网络是超级计算机体系结构的重要组成部分。文中利用正则图连通圈网络模型，设计出了新模型k次Petersen连通圈网络PGCC(k)，它是3正则3连通的，且具有其他好的性质。本文对它的圈因子分解、Hamilton性和一些基本性质进行了研究，并证明了PGCC(1)可分解为边不交的两个等长圈和一个完美对集的并。
Interconnected networks are an important part of supercomputer architecture. In the paper, using the regular graph connected circle network model, a new model kth Peterson connected circle network PGCC(k), which is 3-regular 3-connected and has many good properties, is designed. In this paper, we study its circle factorization, Hamiltonianity and some basic properties, and prove that PGCC(1) can be decomposed into two equal circles with non-intersecting edges and a perfect pairwise set of merges.
| [1] | 师海忠. 正则图连通圈: 多种互连网络的统一模型[C]//中国运筹学会. 中国运筹学大会第十届学术交流会文集: 2010年卷. Hong Kong: Global-Link Informatics Limited, 2010: 202-208. |
| [2] | Bondy, J.A. and Murty, U.S.R. (1976) Graph Theory with Applications. Macmillan Press Ltd., London. |
| [3] | 徐俊明. 组合网络理论[M]. 北京: 科学出版社, 2013. |
| [4] | Xu, J.M. (2015) A First Course in Graph Theory. Science Press, Beijing. |
| [5] | 高随祥. 图论与网络流理论[M]. 北京: 高等教育出版社, 2009. |
| [6] | Borse, Y.M. and Saraf, J.B. (2018) Existence of 3-Regular Subgraphs in Cartesian Product of Cycles. AKCE International Journal of Graphs and Combinatorics, 16, 332-342. |
| [7] | Darbinyan, S.K.H. (2019) Sufficient Conditions for Hamiltonian Cycles in Bipartite Digraphs. Discrete Applied Mathematics, 258, 87-96. https://doi.org/10.1016/j.dam.2018.11.024 |
| [8] | 张治成. 十二面体-师连通圈网络及其笛卡尔乘积网络研究[D]: [硕士学位论文]. 兰州: 西北师范大学, 2020. |
| [9] | Chiba, S. (2018) On Degree Sum Conditions for 2-Factors with a Prescribed Number of Cycles. Discrete Applied Mathematics, 341, 2912-2918. https://doi.org/10.1016/j.disc.2018.06.045 |
| [10] | 师海忠. 几类新的笛卡尔乘积互连网络[J]. 计算机科学, 2013, 40(6A): 265-270. |
| [11] | 张治成. 一类特殊笛卡尔乘积网络的泛圈性[J]. 高校应用数学学报A辑, 2022, 37(3): 345-349. |
| [12] | Lv, H.Z. and Wu, T.Z. (2019) Edge-Disjoint Hamiltonian Cycles of Balanced Hypercubes. Information Processing Letters, 144, 25-30. https://doi.org/10.1016/j.ipl.2018.12.004 |
| [13] | Hsu, L.H., Ho, T.Y., Ho, Y.H., et al. (2014) Cycles in Cube-Connected Cycles Graphs. Discrete Applied Mathematics, 167, 163-171. https://doi.org/10.1016/j.dam.2013.11.021 |
| [14] | Li, Q., Shiu, W.C. and Yao, H. (2015) Matching Preclusion for Cube-Connected Cycles. Discrete Applied Mathematics, 190-191, 118-126. https://doi.org/10.1016/j.dam.2015.04.001 |
| [15] | Gao, H., Lv, B.J. and Wang, K.S. (2018) Two Lower Bounds for Generalized 3-Connectivity of Cartesian Product Graphs. Applied Mathematics and Computation, 338, 305-313. https://doi.org/10.1016/j.amc.2018.04.007 |
