1
School of Computer Science and Engineering (SCOPE), VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati AP, India
(arindam84nit@gmail.com)
2
Department of Mathematics, VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati AP, India
(ranjank.nit52@gmail.com)
3
Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco;Regional Center for the Professions of Education and Training (CRMEF),Casablanca-Settat, Morocco
(broumisaid78@gmail.com)
4
School of Electrical Engineering, Vellore Institute of Technology, Chennai, India
(pritambhowmikjan@gmail.com)
Abstract :
The fuzzy graph theory uses a substantial and important role in modelling and structuring many optimization
problems. DIfferent type of uncertainties exist in most of the optimization problems in real lIfe scenarios
due to indeterminate and incomplete information and it is a challenging task for the expert to design those
optimization problems applying fuzzy graph. To design the incomplete, uncertainty and vagueness in graphical
optimization problems, several extensions of graph theoretical ideas are proposed. The idea of neutrosophic
graph plays an important role to manage the uncertainty, linked with the indeterminate and incomplete
data/information of any optimization problem. In this manuscript, we present the idea of regular neutrosophic
graph, strong neutrosophic graph, bipartite neutrosophic graph, regular neutrosophic graph, and regular strong
neutrosophic graph. We also introduce six different operations on neutrosophic graph, viz., cartesian product,
composition, join, direct product, lexicographic and strong product.
Keywords :
Neutrosophic; uncertainty; neutrosophic graph; bipartite neutrosophic graph.
References :
[1] L. A. Zadeh, “Fuzzy sets,” Information and control, vol. 8, no. 3, pp. 338–353, 1965.
[2] F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic
Probability: Neutrsophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability. Infinite
Study, 2005.
[3] G. Ghorai and M. Pal, “Certain types of product bipolar fuzzy graphs,” International Journal of Applied
and Computational Mathematics, vol. 3, no. 2, pp. 605–619, 2017.
[4] H.-L. Yang, Z.-L. Guo, Y. She, and X. Liao, “On single valued neutrosophic relations,” Journal of Intelligent
& Fuzzy Systems, vol. 30, no. 2, pp. 1045–1056, 2016.
[5] J. Ye, “Single-valued neutrosophic minimum spanning tree and its clustering method,” Journal of intelligent
Systems, vol. 23, no. 3, pp. 311–324, 2014.
[6] R. A. Borzooei, H. Rashmanlou, S. Samanta, and M. Pal, “Regularity of vague graphs,” Journal of
Intelligent & Fuzzy Systems, vol. 30, no. 6, pp. 3681–3689, 2016.
[7] S. Naz, H. Rashmanlou, and M. A. Malik, “Operations on single valued neutrosophic graphs with application,”
Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2137–2151, 2017.
| Style | # |
|---|---|
| MLA | Arindam Dey, Ranjan Kumar, Said Broumi, Pritam Bhowmik. "Different Types of Operations on Neutrosophic Graphs." International Journal of Neutrosophic Science, Vol. 19, No. 2, 2022 ,PP. 87-94 (Doi : https://doi.org/10.54216/IJNS.190208) |
| APA | Arindam Dey, Ranjan Kumar, Said Broumi, Pritam Bhowmik. (2022). Different Types of Operations on Neutrosophic Graphs. Journal of International Journal of Neutrosophic Science, 19 ( 2 ), 87-94 (Doi : https://doi.org/10.54216/IJNS.190208) |
| Chicago | Arindam Dey, Ranjan Kumar, Said Broumi, Pritam Bhowmik. "Different Types of Operations on Neutrosophic Graphs." Journal of International Journal of Neutrosophic Science, 19 no. 2 (2022): 87-94 (Doi : https://doi.org/10.54216/IJNS.190208) |
| Harvard | Arindam Dey, Ranjan Kumar, Said Broumi, Pritam Bhowmik. (2022). Different Types of Operations on Neutrosophic Graphs. Journal of International Journal of Neutrosophic Science, 19 ( 2 ), 87-94 (Doi : https://doi.org/10.54216/IJNS.190208) |
| Vancouver | Arindam Dey, Ranjan Kumar, Said Broumi, Pritam Bhowmik. Different Types of Operations on Neutrosophic Graphs. Journal of International Journal of Neutrosophic Science, (2022); 19 ( 2 ): 87-94 (Doi : https://doi.org/10.54216/IJNS.190208) |
| IEEE | Arindam Dey, Ranjan Kumar, Said Broumi, Pritam Bhowmik, Different Types of Operations on Neutrosophic Graphs, Journal of International Journal of Neutrosophic Science, Vol. 19 , No. 2 , (2022) : 87-94 (Doi : https://doi.org/10.54216/IJNS.190208) |