KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 1

Detour $g$-interior nodes and detour $g$-boundary nodes in bipolar fuzzy graph with applications

Soumitra Poulik(Vidyasagar University)0000-0003-3394-7658
Ganesh Ghorai(Vidyasagar University)0000-0002-3877-8059
Sayfa
—
Yayın Tarihi
2020-02-06
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Applications of detour $g$-distance, detour $g$-boundary node, detour $g$-interior node are given.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we obtain a characterization of bipolar fuzzy detour $g$-eccentric node.
📊
Temel Bulgular & Veri:The concepts of bipolar fuzzy detour $g$-boundary nodes and bipolar fuzzy detour $g$-interior nodes in a bipolar fuzzy graph are examined.
💡
Sonuç & Katkı:Applications of detour $g$-distance, detour $g$-boundary node, detour $g$-interior node are given.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Bipolar fuzzy detour g-distance · bipolar fuzzy detour g-interior node · bipolar fuzzy detour g-boundary node

Abstract

In this paper, we obtain a characterization of bipolar fuzzy detour $g$-eccentric node. The concepts of bipolar fuzzy detour $g$-boundary nodes and bipolar fuzzy detour $g$-interior nodes in a bipolar fuzzy graph are examined. Also we establish the relationship between bipolar fuzzy cut node and bipolar fuzzy detour $g$-boundary node. Some properties of bipolar fuzzy detour $g$-boundary nodes, bipolar fuzzy detour $g$-interior nodes and bipolar fuzzy complete nodes are discussed. Bipolar fuzzy detour $g$-interior node and bipolar fuzzy detour $g$-boundary node of a bipolar fuzzy tree are introduced using maximum bipolar fuzzy spanning tree. Applications of detour $g$-distance, detour $g$-boundary node, detour $g$-interior node are given.

🔖

Bu Makaleye Atıf Yap

Poulik, S., Ghorai, G. (2020). Detour $g$-interior nodes and detour $g$-boundary nodes in bipolar fuzzy graph with applications. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 1. https://doi.org/10.15672/HJMS.2019.666

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (44)

  1. M. Akram and B. Davvaz, Bipolar fuzzy graphs, Inform. Sci. 181 (24), 5548–5564, 2011.
  2. M. Akram and A. Farooq, Bipolar fuzzy tree, New Trends in Mathematical Science, 4 (3), 58–72, 2016.
  3. M. Akram and M.G. Karunambigal, Metric in bipolar fuzzy graphs, World Appl. Sci. J. 14 (12), 1920–1927, 2011.
  4. K.R. Bhutani and A. Rosenfeld, Strong arc in fuzzy graphs, Inform. Sci. 152, 319–322, 2003.
  5. K.R. Bhutani and A. Rosenfeld, Fuzzy end node in fuzzy graphs, Inform. Sci. 152, 323–326, 2003.
  6. R.A. Borzooei and H. Rashmanlou, Caley interval-valued fuzzy graphs, U. P. B. Sci. Bull. Series A, 78 (3), 83–94, 2016.
  7. R.A. Borzooei and H. Rashmanlou, New concepts of vague graphs, Int. J. Mach. Learn. Cybernet. 8, (4) 1081-1092, 2017.
  8. G. Chatrand, D. Erwin, G.L. Johns and P. Zang, Boundary vertices in graphs, Dis- crete Math. 263 (1-3), 25–34, 2003.
  9. G. Chatrand, H. Escuadro and P. Zhang, Detour distance in graph, J. Combin. Math. Combin. Comput. 53, 75–94, 2005.
  10. G. Chatrand, G.L. Johns and P. Zhang, Detour number of a graph, Util. Math. 64, 97–113, 2003.
  11. G. Chartrand and Z. Ping, Introduction to graph theory, Tata McGraw-Hill Edition, 2006.
  12. G. Chartrand and P. Zhang, Distance in graphs-taking the long view, AKCE Int. J. Graphs Comb. 1 (1), 1–13, 2004.
  13. G. Ghorai and M. Pal, On some operations and density of m-polar fuzzy graphs, Pac. Sci. Rev. A: Natur. Sci. Eng. 17 (1), 14–22, 2015.
  14. G. Ghorai and M. Pal, Faces and dual of m-polar fuzzy planar graphs, J. Intell. Fuzzy Syst. 31 (3), 2043–2049, 2016.
  15. G. Ghorai and M. Pal, Certain types of product bipolar fuzzy graphs, Int. J. Appl. Comput. Math. 3 (2), 605–619, 2017.
  16. G. Ghorai and M. Pal, A note on “Regular bipolar fuzzy graphs” Neural Computing and Applications 21(1) 2012 197-205, Neural Comput. Appl. 30 (5), 1569-1572, 2018.
  17. G. Ghorai, S. Sahoo and M. Pal, Certain graph parameters in bipolar fuzzy environ- ment, Int. J. Adv. Intell. Paradigms, doi:10.1504/IJAIP.2018.10024070
  18. J.P. Linda and M.S. Sunitha, On g-eccentric nodes g-boundary nodes and g-interior nodes of a fuzzy graph, Int. J. Math. Sci. Appl. 2 (2), 697–707, 2012.
  19. J.P. Linda and M.S. Sunitha, Fuzzy detour g-interior nodes and fuzzy detour g- boundary nodes of a fuzzy graphs, J. Intell. Fuzzy Syst. 27, 435–442, 2014.
  20. J.P. Linda and M.S. Sunitha, Fuzzy detour g-centre in fuzzy graphs, Ann. Fuzzy Math. Informa. 7 (2), 219–228, 2014.
  21. K.M. Lee, Bipolar-valued fuzzy sets and their basic operations, Proc. Int. Conf. Bangkok, Thailand, 307–317, 2000.
  22. S. Mandal, S. Sahoo, G. Ghorai and M. Pal, Genus value of m-polar fuzzy graphs, J. Intell. Fuzzy Syst. 34 (3), 1947–1957, 2018.
  23. S. Mathew and M.S. Sunitha, Types of arc in fuzzy graph, Inform. Sci. 179, 1760– 1768, 2009.
  24. S. Mathew, M.S. Sunitha and N. Anjali, Some connectivity in bipolar fuzzy graphs, Ann. Pure Appl. Math. 7 (2), 98–100, 2014.
  25. J.N. Mordeson and C.S. Peng, Operation on fuzzy graphs, Inform. Sci. 79, 159–170, 1994.
  26. T. Pramanik, M. Pal, S. Mondal and S. Samanta, A study on bipolar fuzzy planar graph and its application in image shrinking, J. Intell. Fuzzy Syst. 34 (3), 1863–1874, 2018.
  27. T. Pramanik, S. Samanta and M. Pal, Interval-valued fuzzy planar graphs, Int. J. Mach. Learn. Cybernet. 7 (4), 653–664, 2016.
  28. T. Pramanik, S. Samanta, M. Pal and B. Sarkar, Interval-valued fuzzy ϕ-tolerance competition graphs, SpringerPlus, 5, 1–19, 2016.
  29. T. Pramanik, S. Samanta, B. Sarkar and M. Pal, Fuzzy ϕ-tolerance competition graphs, Soft Comput. 21 (13), 3723–3734, 2017.
  30. H. Rashmanlou and R.A. Borzooei, Product vague graphs and Its Applications, J. Intell. Fuzzy Syst. 30, 371–382, 2016.
  31. H. Rashmanlou and R.A. Borzooei, New concepts of Interval-valued Intuitionistic (S, T)-Fuzzy Graphs, Intell. Fuzzy Syst. 30, 1893–1901, 2016.
  32. H. Rashmanlou and M. Pal, Some properties of highly irregular interval-valued fuzzy graphs, World Appl. Sci. J. 27 (12), 1756–1773, 2013.
  33. H. Rashmanlou, S. Samanta, M. Pal and R.A. Borzooei, Intuitionistic fuzzy graphs with categorical properties, Fuzzy Inform. Eng. 7, 317–334, 2015.
  34. H. Rashmanlou, S. Samanta, M. Pal and R.A. Borzooei, Bipolar fuzzy graphs with categorical properties, Int. J. Comput. Intell. Syst. 8 (5), 808–818, 2015.
  35. H. Rashmanlou, S. Samanta, M. Pal and R.A. Borzooei, Product of Bipolar fuzzy graphs and their degrees, Int. J. Gen. Syst. 45 (1), 1–14, 2016.
  36. A. Rosenfield, Fuzzy graphs, in: Fuzzy Sets and Their Application (L. A. Zadeh, K. S. Fu, M. Shimura, Eds.), 77–95, Academic press, New York, 1975.
  37. S. Sahoo and M. Pal, Different types of products on intuitionistic fuzzy graphs, Pac. Sci. Rev. A: Natur. Sci. Eng. 17 (3), 87-96, 2015.
  38. S. Sahoo and M. Pal, Intuitionistic fuzzy tolerance graph with application, J. Appl. Math. Comput. 55, 495-511, 2016.
  39. S. Sahoo and M. Pal, Certain types of edge irregular intuitionistic fuzzy graphs, J. Intell. Fuzzy Syst. 34 (1), 295–305, 2018.
  40. K. Sameena and M.S. Sunitha, A characterization of g-self centered fuzzy graphs, J. Fuzzy Math. 16 (4), 787–791, 2008.
  41. H.L. Yang, S.G. Li, W.H. Yang and Y. Lu, Notes on bipolar fuzzy graphs, Inform. Sci. 242, 113–121, 2013.
  42. L.A. Zadeh, Fuzzy sets, Inform. Control, 8, 338–353, 1965.
  43. W.R. Zhang, Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis, Proc. IEEE Conf. 305–309, 1994.
  44. W.R. Zhang, Bipolar fuzzy sets, Proc. FUZZ-IEEE, 835–840, 1998.