On Null Vertex in Fuzzy Graphs

Main Article Content

M.P. Sunil, J. Suresh Kumar


We introduce a new type of vertex in fuzzy graphs, namely null vertex, which is neither a boundary vertex nor an interior vertex. Here, we initiate a study on the null vertex in fuzzy graphs, explore its properties and establish its presence in various types of fuzzy graphs.

Article Details


  1. K.R. Bhutani, A. Rosenfeld, Fuzzy End Nodes in Fuzzy Graphs, Inf. Sci. 152 (2003), 323–326. https://doi.org/10.1016/s0020-0255(03)00078-1.
  2. G. Chartrand, P. Zhang, A First Course in Graph Theory, Graph Theory, Dover Publications, New York, (2012).
  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. F. Harary, Graph Theory, Addison-Wesley, Boston, (1969).
  5. J.N. Mordeson, P.S. Nair, Fuzzy Graphs and Fuzzy Hypergraphs, Physica Verlag, Berlin, (2000).
  6. J.N. Mordeson, Y.Y. Yao, Fuzzy Cycles and Fuzzy Trees, J. Fuzzy Math. 10 (2002), 189–202.
  7. A. Rosenfeld, Fuzzy Graphs, In: L.A. Zadeh, K.S. Fu, M. Shimura (Eds), Fuzzy Sets and Their Application to Cognitive and Decision Processes, Academic Press, New York, (1975), 77–95.
  8. G.F. Simmons, Introduction to topology and modern analysis, McGraw Hill, New York, (1963).
  9. 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.
  10. M. Tom, M.S. Sunitha, Strong Sum Distance in Fuzzy Graphs, SpringerPlus. 4 (2015), 214. https://doi.org/10.1186/s40064-015-0935-5.
  11. L.A. Zadeh, Fuzzy Sets, Inf. Control. 8 (1965), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.