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Connected Square Network Graphs

Year 2022, Volume: 5 Issue: 2, 57 - 63, 30.06.2022
https://doi.org/10.32323/ujma.1058116

Abstract

In this study, connected square network graphs are introduced and two different definitions are given. Firstly, connected square network graphs are shown to be a Hamilton graph. Further, the labelling algorithm of this graph is obtained by using gray code. Finally, its topological properties are obtained, and conclusion are given.

References

  • [1] A. El-Amawy, S. Latifi, Properties and performance of folded hypercubes, IEEE Trans. Parallel Distrib. Syst., 2(1) (1991), 31-42.
  • [2] H. Y. Chang, R. J. Chen, Incrementally extensible folded hypercube graphs, J. Inf. Sci. Eng., 16(2), (2000), 291-300.
  • [3] Q. Dong, X. Yang, J. Zhao, Y. Y. Tang, Embedding a family of disjoint 3D meshes into a crossed cube, Inf. Sci. 178 (2008), 2396-2405.
  • [4] K. Efe, The crossed cube architecture for parallel computation, IEEE Trans. Parallel Distrib. Syst., 40 (1991), 1312-1316.
  • [5] C. J. Lai, C. H. Tsai, H. C. Hsu, T. K. Li, A dynamic programming algorithm for simulation of a multi-dimensional torus in a crossed cube, Inf. Sci., 180 (2010), 5090-5100.
  • [6] M. Abd-El-Barr, T. F. Soman, Topological properties of hierarchical interconnection networks a review and comparison, J. Electr. Comput. Eng., (2011).
  • [7] K. Chose, K. R. Desai, Hierarchical cubic networks, IEEE Trans. Parallel Distrib. Syst., 6 (1995), 427-435.
  • [8] A. Karci, Hierarchical extended Fibonacci cubes, Iran. J. Sci. Technol. Trans. B Eng., 29 (2005), 117-125.
  • [9] A. Karci, Hierarchic graphs based on the Fibonacci numbers, Istanbul Univ. J. Electr. Electron. Eng., 7(1) (2007), 345-365.
  • [10] A. Karcı, B. Selc¸uk, A new hypercube variant: Fractal Cubic Network Graph, Eng. Sci. Technol. an Int. J., 18(1) (2014), 32-41.
  • [11] B. Selc¸uk, A. Karcı, Connected cubic network graph, Eng. Sci. Technol. an Int. J., 20(3) (2017), 934-943.
  • [12] E. D. Knuth, Generating all n-tuples, The Art of Computer Programming, Volume 4A: Enumeration and Backtracking, Pre-Fascicle 2a, 2004.
  • [13] G. Caporossi, I. Gutman, P. Hansen, L. Pavlovi´c, Graphs with maximum connectivity index, Comput. Biol. Chem., 27(1) (2003), 85-90.
Year 2022, Volume: 5 Issue: 2, 57 - 63, 30.06.2022
https://doi.org/10.32323/ujma.1058116

Abstract

References

  • [1] A. El-Amawy, S. Latifi, Properties and performance of folded hypercubes, IEEE Trans. Parallel Distrib. Syst., 2(1) (1991), 31-42.
  • [2] H. Y. Chang, R. J. Chen, Incrementally extensible folded hypercube graphs, J. Inf. Sci. Eng., 16(2), (2000), 291-300.
  • [3] Q. Dong, X. Yang, J. Zhao, Y. Y. Tang, Embedding a family of disjoint 3D meshes into a crossed cube, Inf. Sci. 178 (2008), 2396-2405.
  • [4] K. Efe, The crossed cube architecture for parallel computation, IEEE Trans. Parallel Distrib. Syst., 40 (1991), 1312-1316.
  • [5] C. J. Lai, C. H. Tsai, H. C. Hsu, T. K. Li, A dynamic programming algorithm for simulation of a multi-dimensional torus in a crossed cube, Inf. Sci., 180 (2010), 5090-5100.
  • [6] M. Abd-El-Barr, T. F. Soman, Topological properties of hierarchical interconnection networks a review and comparison, J. Electr. Comput. Eng., (2011).
  • [7] K. Chose, K. R. Desai, Hierarchical cubic networks, IEEE Trans. Parallel Distrib. Syst., 6 (1995), 427-435.
  • [8] A. Karci, Hierarchical extended Fibonacci cubes, Iran. J. Sci. Technol. Trans. B Eng., 29 (2005), 117-125.
  • [9] A. Karci, Hierarchic graphs based on the Fibonacci numbers, Istanbul Univ. J. Electr. Electron. Eng., 7(1) (2007), 345-365.
  • [10] A. Karcı, B. Selc¸uk, A new hypercube variant: Fractal Cubic Network Graph, Eng. Sci. Technol. an Int. J., 18(1) (2014), 32-41.
  • [11] B. Selc¸uk, A. Karcı, Connected cubic network graph, Eng. Sci. Technol. an Int. J., 20(3) (2017), 934-943.
  • [12] E. D. Knuth, Generating all n-tuples, The Art of Computer Programming, Volume 4A: Enumeration and Backtracking, Pre-Fascicle 2a, 2004.
  • [13] G. Caporossi, I. Gutman, P. Hansen, L. Pavlovi´c, Graphs with maximum connectivity index, Comput. Biol. Chem., 27(1) (2003), 85-90.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Burhan Selçuk

Publication Date June 30, 2022
Submission Date January 15, 2022
Acceptance Date June 1, 2022
Published in Issue Year 2022 Volume: 5 Issue: 2

Cite

APA Selçuk, B. (2022). Connected Square Network Graphs. Universal Journal of Mathematics and Applications, 5(2), 57-63. https://doi.org/10.32323/ujma.1058116
AMA Selçuk B. Connected Square Network Graphs. Univ. J. Math. Appl. June 2022;5(2):57-63. doi:10.32323/ujma.1058116
Chicago Selçuk, Burhan. “Connected Square Network Graphs”. Universal Journal of Mathematics and Applications 5, no. 2 (June 2022): 57-63. https://doi.org/10.32323/ujma.1058116.
EndNote Selçuk B (June 1, 2022) Connected Square Network Graphs. Universal Journal of Mathematics and Applications 5 2 57–63.
IEEE B. Selçuk, “Connected Square Network Graphs”, Univ. J. Math. Appl., vol. 5, no. 2, pp. 57–63, 2022, doi: 10.32323/ujma.1058116.
ISNAD Selçuk, Burhan. “Connected Square Network Graphs”. Universal Journal of Mathematics and Applications 5/2 (June 2022), 57-63. https://doi.org/10.32323/ujma.1058116.
JAMA Selçuk B. Connected Square Network Graphs. Univ. J. Math. Appl. 2022;5:57–63.
MLA Selçuk, Burhan. “Connected Square Network Graphs”. Universal Journal of Mathematics and Applications, vol. 5, no. 2, 2022, pp. 57-63, doi:10.32323/ujma.1058116.
Vancouver Selçuk B. Connected Square Network Graphs. Univ. J. Math. Appl. 2022;5(2):57-63.

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