On Null Vertex in Bipolar Fuzzy Graphs

Main Article Content

M.P. Sunil, J. Suresh Kumar

Abstract

We present a novel vertex in Bipolar fuzzy graph, null vertex, which is distinct from boundary vertex and interior vertex and also attempt a study on null vertex in bipolar fuzzy closed helm graph CHn.

Article Details

References

  1. M. Akram, Bipolar Fuzzy Graphs, Inf. Sci. 181 (2011), 5548–5564. https://doi.org/10.1016/j.ins.2011.07.037.
  2. M. Akram, M.G. Karunambigai, Metric in Bipolar Fuzzy Graphs, World Appl. Sci. J. 14 (2011), 1920–1927.
  3. G. Chartrand, D. Erwin, G.L. Johns, P. Zhang, Boundary Vertices in Graphs, Discr. Math. 263 (2003), 25–34. https://doi.org/10.1016/s0012-365x(02)00567-8.
  4. G. Chartrand, P. Zhang, A First Course in Graph Theory, Dover Publications, New York, 2012.
  5. M. Tom, M.S. Sunitha, Boundary and Interior Nodes in a Fuzzy Graph Using Sum Distance, Fuzzy Inf. Eng. 8 (2016), 75–85. https://doi.org/10.1016/j.fiae.2015.07.001.
  6. A. Rosenfeld, Fuzzy Graphs, In: L.A. Zadeh, K.S. Fu, M. Shimura (Eds), Fuzzy Sets and Their Applications to Cognitive and Decision Processes, Academic Press, New York, pp. 77–95, 1975. https://doi.org/10.1016/B978-0-12-775260-0.50008-6.
  7. M.P. Sunil, J. Suresh Kumar, On D-Distance and D-Closed Graphs, Mapana J. Sci. 22 (2023), 187–193.
  8. M.P. Sunil, J. Suresh Kumar, On Null Vertex in Fuzzy Graphs, Int. J. Anal. Appl. 22 (2024), 43. https://doi.org/10.28924/2291-8639-22-2024-43.
  9. M.P. Sunil, J. Suresh Kumar, Boundary Nodes and Interior Nodes in Bipolar Fuzzy Graphs, Int. J. Res. Appl. Sci. Eng. Technol. 8 (2020), 3035–3040. https://doi.org/10.22214/ijraset.2020.5508.
  10. L.A. Zadeh, Fuzzy Sets, Inf. Control. 8 (1965), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.