Regular Interval-Valued Intuitionistic Fuzzy Graphs

S. N. Mishra, A. Pal

Abstract


In this paper, we introduce Regular Interval-Valued Intuitionistic Fuzzy Graphs (RIVIFG) and investigate some of their attributes. We talk about some conditions for regularity of an interval-valued intuitionistic fuzzy graph and obtain \(f\)-morphism on an interval-valued intuitionistic fuzzy graph and regular interval-valued intuitionistic fuzzy graph. \((2, k)\)-regular and totally \((2, k)\)-regular interval-valued intuitionistic fuzzy graphs are some elegant properties.

Keywords


Intuitionistic fuzzy graph(IFG); \(f\)-morphism; \((2, k)\)-regular graph

Full Text:

PDF

References


M. Akram and W.A. Dudek, Interval-valued fuzzy graphs, Computers and Mathematics with Applications 61 (2011), 289–299.

M. Akram and B. Davvaz, Strong intuitionistic fuzzy graphs, Filomat 26 (1) (2012), 177–196.

K. Atanassov and G. Gargov, Interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems 31 (1989), 343–349.

K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87–96.

K.T. Atanassov, Intuitionistic fuzzy sets: Theory, applications, Studies in Fuzziness and Soft Computing, Heidelberg, New York, Physica-Verl. (1999).

S.N. Mishra and A. Pal, Product of interval-valued intuitionistic fuzzy graph, Annals of Pure and Applied Mathematics 4 (2) (2013), 138–144.

A. Nagoor Gani and K. Radha, On regular fuzzy graphs, Journal of Physical Science 12 (2008), 33–40.

A. Northup, A Study of Semi-regular Graphs, Bachelors Thesis, Stetson University, 2002.

R. Parvathi and M.G. Karunambigai, Intuitionistic fuzzy graphs, Computational Intelligence, Theory and Applications (2006), pp. 139–150, doi:10.1007/3-540-34783-6_15.

A. Rosenfeld, Fuzzy graphs, Fuzzy Sets and their Applications, L.A. Zadeh, K.S. Fu and M. Shimura (eds.), Academic Press, New York (1975), pp. 77–95.

N.R. Santhi Maheswari and C. Sekar, ((r,2, r(r-1)))-regular graphs, International Journal of Mathematics and soft Computing 2 (2) (2012), 25–33.

N.R. Santhi Maheswari and C. Sekar, On (d_2) of a vertex in Product of Graphs, One-Day International Conference on Recent Trends in Discrete Mathematics and its of Applications to Science and Engineering (ICODIMA 2013), December 3, 2013.

R. Seethalakshmi and R.B. Gnanajothi, Regularity conditions on an intuitionistic fuzzy graph, Applied Mathematical Sciences 7 (105) (2013), 5225–5234.

L.A. Zadeh, The concept of a linguistic and application to approximate reasoning I, Information Sci. 8 (1975), 199–249.




DOI: http://dx.doi.org/10.26713%2Fjims.v9i3.764

eISSN 0975-5748; pISSN 0974-875X