1318 777
Full Length Article
International Journal of Neutrosophic Science
Volume 5 , Issue 1, PP: 38-58 , 2020 | Cite this article as | XML | Html |PDF


Dominating Energy in Neutrosophic graphs

Authors Names :   M. Mullai   1 *     Said Broumi   2  

1  Affiliation :  Department of Mathematics(DDE), Alagappa University, Karaikudi, Tamilnadu, India

    Email :  mullaim@alagappauniversity.ac.in

2  Affiliation :  Laboratory of Information processing, Faculty of Sciences , Ben M’SiK, University Hassan II,B.P 7955, Sidi Othman, Casablanca, Morocco

    Email :  broumisaid78@gmail.com

Doi   :   https://doi.org/10.54216/IJNS.050104

Abstract :

Dominating energy of graphs plays a vital role in the field of application in energy. Results by applying neutrosophic graph theory is more efficient than other existing methods. So, dominating energy of neutrosophic graphs will also give more accurate results than other exixting methods in the field of energy. This article introduces dominating energy of neutrosophic graphs. Dominating energy of a neutrosophic graph, dominating neutrosophic adjacency matrix, eigen values for the dominating energy of a neutrosophic graphs and complement of neutrosophic graphs are defined with examples. Also, dominating energy in union and join operations of neutrosophic graphs are developed and some theorems in dominating energy of a neutrosophic graphs are derived here.

Keywords :

Neutrosophic graph , dominating energy of neutrosophic graph , eigen values for dominating energy of a neutrosophic graph.

References :

[1]       Cockayne.E.J and Hedetnieme, S.T,Towards a Theory of Domination in Graphs, Networks 7, pp.247-261, 1977.

[2]       De Jaenisch, C.F.Applications de l’Analyze Mathematique an Jendes Echecs, 1862.

[3]       Gutman.I, The Energy of a graph, Ber.Math-Statist.Sekt.Forschungsz.Graz, 103 ,pp.1-22, 1978.

[4]       Nagoorgani.A and Chandrasekaran.V.T, Domination in Fuzzy Graph, Advances in Fuzzy sets and systems,1(1),pp.17-26, (2006).

[5]       Parvathi.R, Karumbigai.M.G. Intuitionistic fuzzy graphs, Notes on Instuitionistic Fuzzy Sets 18(4),pp.48-58, 2012.

[6]       Parvathi.R and G.Thamizhendhi, Domination in intuitionistic fuzzy graphs, Fourth Int.Conf.on IFSs, Sofia, 15-16 May 2010,NIFS Vol.16(2),pp.39-49, 2010.

[7]       Peide Liu, Qaisar Khan, Jun Ye & Tahir Mahmood., Group Decision-Making Method Under Hesitant Interval Neutrosophic Uncertain Linguistic Environment, International Journal of Fuzzy Systems, 20(7), pp.2337-2353, 2018. 

[8]       Praba.B, Chandrasekaran.V.M, Deepa.G, Energy of an Intuitionistic fuzzy graph of Italin journal of pure and applied mathematics-N.32,pp.431-444, 2014.

[9]       Qaisar khan, Tahir mahmood and Jun ye., Multiple Attribute Decision-Making Method under Hesitant Single Valued Neutrosophic Uncertain Linguistic Environment, Journal of Inequalities and Special Functions, 8(2), pp.1-17 ,2017. 

[10]     Qaisar Khan, Nasruddin Hassan and Tahir Mahmood, Neutrosophic Cubic Power Muirhead Mean Operators with Uncertain Data for Multi-Attribute Decision Making, Symmetry,10 , 444, 2018.

[11]     Ranjan Kumar , S A Edaltpanah , Sripati Jha , Said Broumi and Arindam Dey, “Neutrosophic Shortest Path Problem ”, Neutrosophic sets and systems, Vol.23, pp.5-15, 2018.

[12]     Rosenfeld.A, Fuzzy Graphs, in Zadeh.L.A, Fu.K.CS, Tanaka.K and Shimura.M(eds), Fuzzy Sets and their Applications to Cognitive and Decision Process,Academic Press, New York,pp.75-95, 1975.

[13]     S Broumi et. al., Single valued Neutrosophic graphs, Journal of New Theory,10, pp.86-101,2016.

[14]     S Broumi, Arindam Dey, M Talea, A Bakali, F Smarandache, D Nagarajan, “Shortest path problem using Bellman algorithm under neutrosophic environment”, Complex & Intelligent Systems 5 (4), pp.409-416

[15]     S. Broumi, A.Bakali, F. Smarandache, P. K.Singh, and Arindam Dey” Single Valued (2n+1) Sided Polygonal Neutrosophic Numbers and Single Valued (2n) Sided Polygonal Neutrosophic Numbers” Neutrosophic sets and systems, 2019

[16]     S Broumi, Arindam Dey, A Bakali, M Talea, F Smarandache, LH Son, D Koley, “Uniform Single Valued Neutrosophic Graphs”, Neutrosophic sets and systems, Vol.17, pp.42-49, 2017.

[17]     Somasundaram.A and Somasundaram.S., Domination in fuzzy graphs-1, Pattern Recognition Letters,19(9), pp.787-791,1998.

[18]     Tahir Mahmood & Qaisar Khan,  Interval Neutrosophic finite switchboard state machine, Afrika Matematika, 27, pp.1361-1376, 2016.

[19]     Vijayraghavan, A.Kaleemulla and S.ShariefBasha, Dominating energy in products of Intuitionistic fuzzy graphs of Global Pharma Technology, Vol.9,Issue 6, pp.64-76.

[20]     Zadeh.L.A, Fuzzy sets, Information and Control,8, pp.338-353, 1965.

[21]     Mullai.M., Domination in neutrosophic graphs, Neutrosophic Graph Theory and Algorithms, IGI Global Publications, U.S.A., ISBN 9781799813149, pp.131-147, 2019.

[22]     S. Broumi, L.H. Son, A. Bakali, M. Talea, F. Smarandache, G. Selvachandran, Computing Operational Matrices in Neutrosophic Environments: A Matlab Toolbox, Neutrosophic Sets and Systems, Vol. 18, 58-66, 2017,

[23]     S. Broumi, A. Dey, M. Talea, A. Bakali, F. Smarandache, D. Nagarajan, M. Lathamaheswari and R. Kumar, Shortest Path Problem using Bellman Algorithm under Neutrosophic Environment, Complex & Intelligent Systems, 5, 409–416, 2019, https://doi.org/10.1007/s40747-019-0101-8, 

[24]     S. Broumi, M.Talea, A. Bakali, F. Smarandache, D.Nagarajan, M. Lathamaheswari and M.Parimala, Shortest path problem in fuzzy, intuitionistic fuzzy and neutrosophic environment: an overview, Complex & Intelligent Systems, 5, 371–378, 2019. https://doi.org/10.1007/s40747-019-0098-z

[25]     S.Broumi,D. Nagarajan, A. Bakali, M. Talea, F. Smarandache, M. Lathamaheswari, The shortest path problem in interval valued trapezoidal and triangular neutrosophic environment, Complex & Intelligent Systems, 5, 391–402, 2019 .https://doi.org/10.1007/s40747-019-0092-5

[26]     S. A. Edalatpanah, A Direct Model for Triangular Neutrosophic Linear Programming, International Journal of Neutrosophic Science, Volume 1 , Issue 1, pp. 19-28, 2020

[27]     Akbar Rezaei, Florentin Smarandache ,On Neutro-BE-algebras and Anti-BE-algebras, International Journal of Neutrosophic Science, Volume 4 , Issue 1, pp. 08-15, 2020

[28]     M.A. Ibrahim, A.A.A. Agboola , E.O. Adeleke, S.A. Akinleye, On Neutrosophic Quadruple Hypervector Spaces, International Journal of Neutrosophic Science, Volume 4 , Issue 1, PP: 20-35, 2020


Cite this Article as :
M. Mullai , Said Broumi, Dominating Energy in Neutrosophic graphs, International Journal of Neutrosophic Science, Vol. 5 , No. 1 , (2020) : 38-58 (Doi   :  https://doi.org/10.54216/IJNS.050104)