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Research Article

Optimal layout of recursive circulant graphs

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Pages 209-219 | Received 26 Mar 2021, Accepted 23 Jul 2021, Published online: 12 Aug 2021

References

  • K.A.S. Abdel-Ghaffar, Maximum number of edges joining vertices on a cube, Inform. Process. Lett. 87(2) (2003), pp. 95–99.
  • T. Araki and Y. Shibata, Pancyclicity of recursive circulant graphs, Inform. Process. Lett. 81 (2002), pp. 187–190.
  • J.C. Bermond, F. Comellas, and D.F. Hsu, Distributed loop computer networks: A survey, J. Parallel Distrib. Comput. 24(1) (1995), pp. 2–10.
  • S.L. Bezrukov, J.D. Chavez, L.H. Harper, M. Röttger, and U.P. Schroeder, International Symposium on Mathematical Foundations of Computer Science MFCS. Embedding of hypercubes into grids, MFCS, 1998, pp. 693–701.
  • S. Bezrukov, S. Das, and R. Elssser, An edge-isoperimetric problem for powers of the Petersen graph, Ann. Comb. 4(2) (2000), pp. 153–169.
  • F.T. Boesch and J. Wang, Reliable circulant networks with minimum transmission delay, IEEE Trans. Circuits Syst. 32(12) (1985), pp. 1286–1291.
  • C.K. Cheng, Linear placement algorithms and applications to VLSI design, Networks 17 (1987), pp. 439–464.
  • S.A. Choudum and U. Nahdini, Complete binary trees in folded and enhanced cubes, Networks 43(4) (2004), pp. 266–272.
  • J. Diaz, J. Petit, and M. Serna, A survey of graph layout problems, ACM Comput. Surveys 34(3) (2002), pp. 313–356.
  • S. El-Basil, Applications of caterpillar trees in chemistry and physics, J. Math. Chem. 1(2) (1987), pp. 153–174.
  • S. El-Basil, Caterpillar (Gutman) trees in chemical graph theory, in Advances in the Theory of Benzenoid Hydrocarbons, Topics in Current Chemistry, I. Gutman and S. J. Cyvin, eds., Vol. 153, 1990, pp. 273–289.
  • M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman & Co., New York, 1979.
  • I. Gutman, Topological properties of benzenoid systems, Theor. Chim. Acta 45(4) (1977), pp. 309–315.
  • F. Harary and A.J. Schwenk, The number of caterpillars, Discrete Math. 6(4) (1973), pp. 359–365.
  • L.H. Harper, Optimal assignment of numbers to vertices, J. Soc. Indust. Appl. Math. (SIAM) 12(1) (1964), pp. 131–135.
  • L.H. Harper, Global Methods for Combinatorial Isoperimetric Problems, 1st ed., The Press Syndicate of the University of the Cambridge, New York, 2004.
  • S. Horton, The optimal linear arrangement problem: Algorithms and approximation, Ph.D. thesis, Georgia Institute of Technology, 1997.
  • H. Hosoya and F. Harary, On the matching properties of three fence graphs, J. Math. Chem. 12 (1993), pp. 211–218.
  • D.F. Hsu, On container width and length in graphs, groups and networks, IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E-77A (1994), pp. 668–680.
  • R.M. Karp, Mapping the genome: Some combinatorial problems arising in molecular biology, Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, New York, NY: ACM Press, 1993, pp. 278–285.
  • Y-L. Lai and K. Williams, A survey of solved problems and applications on bandwidth edgesum and profile of graphs, J. Graph Theory 31 (1999), pp. 75–94.
  • F.T. Leighton, Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes, 1st ed., Morgan Kaufmann Publishers, San Mateo, California, 1992.
  • H.S. Lim, J.H. Park, and K.Y. Chwa, Embedding trees in recursive circulants, Discrete Appl. Math. 69 (1996), pp. 83–99.
  • B. Mans, Optimal distributed algorithms in unlabeled tori and chordal rings, J. Parallel Distrib. Comput. 46 (1997), pp. 80–90.
  • P. Manuel, I. Rajasingh, B. Rajan, and H. Mercy, Exact wirelength of hypercubes on a grid, Discrete Appl. Math. 157 (2009), pp. 1486–1495.
  • G. Mitchison and R. Durbin, Optimal numberings of an N × N array, SIAM J. Algebr. Discrete Methods 7(4) (1986), pp. 571–582.
  • G.K. Nandini, R.S. Rajan, T.M. Rajalaxmi, A.A. Shantrinal, and S.K.S Husain, Wiener index via wirelength of an embedding, Discrete Math. Algorithms Appl. (2021), p. 2150087.
  • J.H. Park and K.Y. Chwa, Recursive circulant: A new topology for multicomputer networks (extended abstract), Proceedings of the International Symposium on Parallel Architectures, Algorithms and Networks, ISPAZ-94, Kanazava, Japan, 1994, pp. 73–80.
  • J.H. Park and K.Y. Chwa, Fundamental study recursive circulants and their embeddings among hypercubes, Theoret. Comput. Sci. 244 (2000), pp. 35–62.
  • R.S. Rajan, T. Kalinowski, S. Klavzar, H. Mokhtar, and T.M. Rajalaxmi, Lower bounds for dilation, wirelength, and edge congestion of embedding graphs into hypercubes, J. Supercomput. 77(4) (2021), pp. 4135–4150.
  • I. Rajasingh, P. Manuel, M. Arockiaraj, and B. Rajan, Embeddings of circulant networks, J. Comb. Optim. 26(1) (2013), pp. 135–151.
  • I. Rajasingh, P. Manuel, B. Rajan, and M. Arockiaraj, Wirelength of hypercubes into certain trees, Discrete Appl. Math. 160 (2012), pp. 2778–2786.
  • F. Shahrokhi, O. Sýkora, L.A. Székly, and I. Vrto, On bipartite drawings and the linear arrangement problem, Workshop on Algorithms and Data Structures, 1997.
  • R. Sundara Rajan, T.M. Rajalaxmi, J.B. Liu, and G. Sethuraman, Wirelength of embedding complete multipartite graphs into certain graphs, Discrete Appl. Math. 280 (2020), pp. 221–236.
  • J. Xu, Topological Structure and Analysis of Interconnection Networks, Kluwer Academic Publishers, Dordrecht, Netherlands, 2001.
  • T. Yamada and P. Bork, Evolution of biomolecular networks-lessons from metabolic and protein interactions, Nature Rev. Mol. Cell Biol. 10(11) (2009), pp. 791–803.
  • X. Yang, D.J. Evans, and G.M. Megson, Maximum induced subgraph of a recursive circulant, Inform. Process. Lett. 95 (2005), pp. 293–298.

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