Year 2020, Volume 49 , Issue 1, Pages 106 - 119 2020-02-06

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

Soumitra POULİK [1] , Ganesh GHORAİ [2]


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.
Bipolar fuzzy detour g-distance, bipolar fuzzy detour g-interior node, bipolar fuzzy detour g-boundary node
  • [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.
Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0003-3394-7658
Author: Soumitra POULİK
Institution: Vidyasagar University
Country: India


Orcid: 0000-0002-3877-8059
Author: Ganesh GHORAİ (Primary Author)
Institution: Vidyasagar University
Country: India


Dates

Publication Date : February 6, 2020

Bibtex @research article { hujms535188, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {106 - 119}, doi = {10.15672/HJMS.2019.666}, title = {Detour \$g\$-interior nodes and detour \$g\$-boundary nodes in bipolar fuzzy graph with applications}, key = {cite}, author = {POULİK, Soumitra and GHORAİ, Ganesh} }
APA POULİK, S , GHORAİ, G . (2020). Detour $g$-interior nodes and detour $g$-boundary nodes in bipolar fuzzy graph with applications. Hacettepe Journal of Mathematics and Statistics , 49 (1) , 106-119 . DOI: 10.15672/HJMS.2019.666
MLA POULİK, S , GHORAİ, G . "Detour $g$-interior nodes and detour $g$-boundary nodes in bipolar fuzzy graph with applications". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 106-119 <https://dergipark.org.tr/en/pub/hujms/issue/52287/535188>
Chicago POULİK, S , GHORAİ, G . "Detour $g$-interior nodes and detour $g$-boundary nodes in bipolar fuzzy graph with applications". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 106-119
RIS TY - JOUR T1 - Detour $g$-interior nodes and detour $g$-boundary nodes in bipolar fuzzy graph with applications AU - Soumitra POULİK , Ganesh GHORAİ Y1 - 2020 PY - 2020 N1 - doi: 10.15672/HJMS.2019.666 DO - 10.15672/HJMS.2019.666 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 106 EP - 119 VL - 49 IS - 1 SN - 2651-477X-2651-477X M3 - doi: 10.15672/HJMS.2019.666 UR - https://doi.org/10.15672/HJMS.2019.666 Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Detour $g$-interior nodes and detour $g$-boundary nodes in bipolar fuzzy graph with applications %A Soumitra POULİK , Ganesh GHORAİ %T Detour $g$-interior nodes and detour $g$-boundary nodes in bipolar fuzzy graph with applications %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 1 %R doi: 10.15672/HJMS.2019.666 %U 10.15672/HJMS.2019.666
ISNAD POULİK, Soumitra , GHORAİ, Ganesh . "Detour $g$-interior nodes and detour $g$-boundary nodes in bipolar fuzzy graph with applications". Hacettepe Journal of Mathematics and Statistics 49 / 1 (February 2020): 106-119 . https://doi.org/10.15672/HJMS.2019.666
AMA POULİK S , GHORAİ G . Detour $g$-interior nodes and detour $g$-boundary nodes in bipolar fuzzy graph with applications. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 106-119.
Vancouver POULİK S , GHORAİ G . Detour $g$-interior nodes and detour $g$-boundary nodes in bipolar fuzzy graph with applications. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 119-106.