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IDENTIFICATION OF KNIGHTS’ RELATIONS FOR 5×5 KNIGHT GRAPH BY MODULARITY

Cilt: 7 Sayı: 13 28 Aralık 2020
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IDENTIFICATION OF KNIGHTS’ RELATIONS FOR 5×5 KNIGHT GRAPH BY MODULARITY

Abstract

Modularity is a widely utilized technic to analyze graphs. The modularity divides the specified network into relational clusters. The clusters highlight the shared properties between the clustered nodes. In the present study, we analyze 5×5 knight graph by modularity to extract 5 Knight Covering Problem (5-KCP) solutions. Our investigation is completed for resolutions from 0.1 to 1.8. The maximum modularity score is 0.3 found for resolution 0.8. Moreover, resolution 0.1 is the best resolution to find more solutions of 5-KCP. Also, the analyses show resolution 1.0 is the best resolution to find the solutions of 5-KCP efficiently. Lastly, modularity extracts the solutions from 1 to 7 out of 172 solutions.

Keywords

Knight graph , Modularity , 5-KCP

Kaynakça

  1. S. Bai, G. Zhu, and J. Huang, "An Intelligent Algorithm for the (1,2,2)-Generalized Knight's Tour Problem," in 2013 Ninth International Conference on Computational Intelligence and Security, 2013, pp. 583-588.
  2. H. Jian and B. Sen, "An Efficient Algorithm for the Generalized (1,k)-Knight's Tours Problem," in 2009 First International Workshop on Education Technology and Computer Science, 2009, vol. 1, pp. 697-701.
  3. P. Hingston and G. Kendall, Ant Colonies Discover Knight's Tours. 2004, pp. 1213-1218.
  4. S. Bai, X. Liao, X. Qu, and Y. Liu, "Generalized Knight's Tour Problem and Its Solutions Algorithm," in 2006 International Conference on Computational Intelligence and Security, 2006, vol. 1, pp. 570-573.
  5. I. Parberry, "An Efficient Algorithm for the Knight's Tour Problem," Discrete Applied Mathematics, vol. 73, pp. 251-260, 03/01 1997.
  6. J. Demaio and B. Mathew, "Which Chessboards have a Closed Knight's Tour within the Rectangular Prism?," Electr. J. Comb., vol. 18, 01/05 2011.
  7. A. Kumar, "Non-crossing Knight's Tour in 3-Dimension," 03/29 2008.
  8. P. Aliquippa and Pennsylvania, "THEMATIC KNIGHT'S TOUR QUOTES," 06/29 2020.
  9. A. Philip, "A Generalized Pseudo-Knight?s Tour Algorithm for Encryption of an Image," IEEE Potentials, vol. 32, no. 6, pp. 10-16, 2013.
  10. J. Kumar and S. Nirmala, "Securing the contents of document images using knight moves and genetic approach," in 2015 International Conference on Advances in Computing, Communications and Informatics (ICACCI), 2015, pp. 1091-1095.

Kaynak Göster

APA
Güldal, S. (2020). IDENTIFICATION OF KNIGHTS’ RELATIONS FOR 5×5 KNIGHT GRAPH BY MODULARITY. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi, 7(13), 104-114. https://izlik.org/JA44LN77LM
AMA
1.Güldal S. IDENTIFICATION OF KNIGHTS’ RELATIONS FOR 5×5 KNIGHT GRAPH BY MODULARITY. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi. 2020;7(13):104-114. https://izlik.org/JA44LN77LM
Chicago
Güldal, Serkan. 2020. “IDENTIFICATION OF KNIGHTS’ RELATIONS FOR 5×5 KNIGHT GRAPH BY MODULARITY”. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi 7 (13): 104-14. https://izlik.org/JA44LN77LM.
EndNote
Güldal S (01 Aralık 2020) IDENTIFICATION OF KNIGHTS’ RELATIONS FOR 5×5 KNIGHT GRAPH BY MODULARITY. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi 7 13 104–114.
IEEE
[1]S. Güldal, “IDENTIFICATION OF KNIGHTS’ RELATIONS FOR 5×5 KNIGHT GRAPH BY MODULARITY”, Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi, c. 7, sy 13, ss. 104–114, Ara. 2020, [çevrimiçi]. Erişim adresi: https://izlik.org/JA44LN77LM
ISNAD
Güldal, Serkan. “IDENTIFICATION OF KNIGHTS’ RELATIONS FOR 5×5 KNIGHT GRAPH BY MODULARITY”. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi 7/13 (01 Aralık 2020): 104-114. https://izlik.org/JA44LN77LM.
JAMA
1.Güldal S. IDENTIFICATION OF KNIGHTS’ RELATIONS FOR 5×5 KNIGHT GRAPH BY MODULARITY. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi. 2020;7:104–114.
MLA
Güldal, Serkan. “IDENTIFICATION OF KNIGHTS’ RELATIONS FOR 5×5 KNIGHT GRAPH BY MODULARITY”. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi, c. 7, sy 13, Aralık 2020, ss. 104-1, https://izlik.org/JA44LN77LM.
Vancouver
1.Serkan Güldal. IDENTIFICATION OF KNIGHTS’ RELATIONS FOR 5×5 KNIGHT GRAPH BY MODULARITY. Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi [Internet]. 01 Aralık 2020;7(13):104-1. Erişim adresi: https://izlik.org/JA44LN77LM