ENERGY OF FUZZY LABELING IN
COMPLETE GRAPH THROUGH
HAMILTONIAN CIRCUIT

S.Vimala; A.Nagarani

doi:https://doi.org/10.14445/22315373/IJMTT-V44P508

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 44 | Number 1 | Year 2017 | Article Id. IJMTT-V44P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V44P508

ENERGY OF FUZZY LABELING IN COMPLETE GRAPH THROUGH HAMILTONIAN CIRCUIT

S.Vimala, A.Nagarani

Abstract

A Hamiltonian circuit includes each vertex of the graph once and only once. This paper generalizing the energy of fuzzy labeling graph of complete graphs through Hamiltonian circuit and studied properties of complete graph. Discussion of upper bound and lower bound of energy.

Keywords

complete graph, fuzzy labeling graph, energy of fuzzy labeling graph, Hamiltonian circuit

References

[1] N .Anjali Narayanan, Sunil Mathew, Energy of a fuzzy graph, Annals of Fuzzy Mathematics and Informatics, (2013) ,Vol 6, No,3. 455 – 465.
[2] R.Balakrishnan, The energy of a graph, Linear Algebra Appl.387 (2004) 287 -295 .
[3] R.B. Bapat and S.Pati, Energy of a graph is never an odd interger, Bull Kerala Math. Asso.1 (2004) 129 -132
[4] W.Du, X.Li and Y.Li,Various energies of random graphs, MATCH Commun. Math. Compute. Chem. . . .64 (2010) 251-260.
[5] I.Gutman and S.Zare Firoozabadi. J.A.de la Prena, J.Rada, On the energy of regular graphs. MATCH Commun. Math. Comput .Chem. 57 (2007) 435-442 .
[6] K.A. Germina and S.Hameed, Thomas Zaslavsky, On products and line graphs of signed graphs, their eigenvalues and energy, Linear Algebra Appl.435 (2011) 2432-2450.
[7] Harary,The book “Graph theory” in Wesley Publication Company 1969.
[8] G.Indulal and A.Vijayakumar, Energies of some non- regular graphs J.Math.Chem. 42 (2007) 377- 386 .
[9] J.N.Mordeson, Fuzzy line graphs, Pattern Recognition Letter 14 (1993) 381- 384.
[10] J.N.Mordeson, and P.S.Nair, Cycles and cocycles of fuzzy graphs, Inform. Sci.90 (1996) 39 -49
[11] A.Nagoorgani, V.T.Chandrasekaran,”A First Look at Fuzzy Graph Theory “in Allied Publishers Pvt. Ltd
[12] A.Nagoorgani , Fuzzy Bipartite graphs , Journal of Quantitative methods, 2 No . 2 (2006), 54-60
[13] A.Nagarani and S.Vimala, Energy Of Fuzzy Labeling Graph EFl(G) –Part II, International Journal of Innovative Research in Science, Engineering and Technology Vol. 5, Issue 9, September 2016
[14] S.Pirzada and I.Gutman, Energy of a graph is never the square root of an odd integer, Appl. Anal.Discrete Math . 2 (2008) 118 – 121.
[15] A.Rosenfield, Fuzzy Graph, In:L.A.Zadeh , K.S.Fu, and M.Shimura,Editors, Fuzzy sets and their Applications to Cognitive and Decision Process Academic Press ,New York ,77 – 95(1975).
[16] I.Shparlinski, On the energy of some circulant graphs, Linear Algebra Appl .414 (2006) 378- 382.
[17] M.S. Sunitha, and A.Vijayakumar , A Characterization of fuzzy trees . Information Science, 113(1999) ,293 – 300.
[18] S.Vimala and A.Nagarani, Energy Of Fuzzy Labeling Graph EFl(G) –Part I,International Journal Of Scientific & Engineering Research, Volume 7, Issue 4, APRIL-2016.
[19] L.A. Zadeh ,Fuzzy sets.Information and control, 8, (1965),338-353.

Citation :

S.Vimala, A.Nagarani, "ENERGY OF FUZZY LABELING IN COMPLETE GRAPH THROUGH HAMILTONIAN CIRCUIT," International Journal of Mathematics Trends and Technology (IJMTT), vol. 44, no. 1, pp. 47-50, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V44P508