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Volume 29, No 4, 2022, P. 59-76 UDC 519.176
Keywords: family of circulant networks of degree six, diameter, extremal circulant graph of degree six, network on a chip. DOI: 10.33048/daio.2022.29.743 Emilia A. Monakhova 1 Received June 1, 2022 References[1] E. A. Monakhova, Series of families of degree six circulant graphs, Prikl. Diskretn. Mat., No. 54, 109–124 (2021).[2] A. Yu. Romanov, A. A. Amerikanov, and E. V. Lezhnev, Analysis of approaches for synthesis of networks-on-chip by using circulant topologies, J. Phys.: Conf. Ser. 1050, ID 012071, 12 p. (2018). [3] E. A. Monakhova, A. Yu. Romanov, and E. V. Lezhnev, Shortest path search algorithm in optimal two-dimensional circulant networks: Implementation for networks-on-chip, IEEE Access. 8, 215010–215019 (2020). [4] E. A. Monakhova, O. G. Monakhov, A. Yu. Romanov, and E. V. Lezhnev, Analytical routing algorithm for networks-on-chip with the three-dimensional circulant topology, in Proc. Moscow Workshop Electron. Netw. Technol., Moscow, Russia, March 11–13, 2020 (Higher School of Economics, Moscow, 2020). [5] F. K. Hwang, A survey on multi-loop networks, Theor. Comput. Sci. 299, 107–121 (2003). [6] E. A. Monakhova, A survey on undirected circulant graphs, Discrete Math. Algorithms Appl. 4 (1), ID 1250002, 30 p. (2012). [7] H. Pérez-Rosés, M. Bras-Amorós, and J. M. Serradilla-Merinero, Greedy routing in circulant networks, Graphs Comb. 38, ID 86, 16 p. (2022). [8] C. Martínez, E. Vallejo, R. Beivide, C. Izu, and M. Moretó, Dense Gaussian networks: Suitable topologies for on-chip multiprocessors, Int. J. Parallel Program. 34, 193–211 (2006). [9] C. Martínez, E. Vallejo, M. Moretó, R. Beivide, and M. Valero, Hierarchical topologies for large-scale two-level networks, in Actas XVI Jornadas Paralelismo, Granada, Spain, Sept. 13–16, 2005 (Paraninfo, Madrid, 2005), pp. 133–140. [10] E. Monakhova, Optimal triple loop networks with given transmission delay: Topological design and routing, in Proc. Int. Network Optimization Conf., Évry/Paris, France, Oct. 27–29, 2003 (Inst. Natl. Télécommun., Évry, 2003), pp. 410–415. [11] R. Dougherty and V. Faber, The degree-diameter problem for several varieties of Cayley graphs I: The abelian case, SIAM J. Discrete Math. 17 (3), 478–519 (2004). [12] X. Huang, A. F. Ramos, and Y. Deng, Optimal circulant graphs as lowlatency network topologies, J. Supercomput. 78, 13491–13510 (2022). [13] R. R. Lewis, Analysis and construction of extremal circulant and other abelian Cayley graphs, PhD thes. (London, 2021). [14] Research problems, J. Comb. Theory. 2 (3), 393 (1967). [15] F. Göbel and E. A. Neutel, Cyclic graphs, Discrete Appl. Math. 99, 3–12 (2000). [16] D.-Z. Du, D. F. Hsu, Q. Li, and J. Xu, A combinatorial problem related to distributed loop networks, Networks 20 (2), 173–180 (1990). [17] B.-X. Chen, J.-X. Meng, andW.-J. Xiao, Some new optimal and suboptimal infinite families of undirected double-loop networks, Discrete Math. Theor. Comput. Sci. 8, 299–312 (2006). [18] D. Tzvieli, Minimal diameter double-loop networks. I. Large infinite optimal families, Networks 21 (4), 387–415 (1991). [19] R. R. Lewis, The degree-diameter problem for circulant graphs of degree 8 and 9, Electron. J. Comb. 21 (4), ID P4.50, 1–19 (2014). [20] R. R. Lewis, The degree-diameter problem for circulant graphs of degrees 10 and 11, Discrete Math. 341 (9), 2553–2566 (2018). [21] C. Dalfó, M. A. Fiol, N. Lopéz, and J. Ryan, An improved Moore bound and some new optimal families of mixed abelian Cayley graphs, Discrete Math. 343 (10), ID 112034, 10 p. (2020). |
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