Different Types of Operations on Neutrosophic Graphs

Arindam; Ranjan; Said; Pritam

doi:https://doi.org/10.54216/IJNS.190208

Full Length Article

Volume 19 • Issue 2 • PP: 87-94 • 2022

Different Types of Operations on Neutrosophic Graphs

Arindam Dey ^1*

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,

Ranjan Kumar ²

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,

Said Broumi ³

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,

Pritam Bhowmik ⁴

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¹School of Computer Science and Engineering (SCOPE), VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati AP, India

²Department of Mathematics, VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati AP, India

³Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco;Regional Center for the Professions of Education and Training (CRMEF),Casablanca-Settat, Morocco

⁴School of Electrical Engineering, Vellore Institute of Technology, Chennai, India

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.190208

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Received: March 19, 2022 Accepted: September 05, 2022

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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.

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Dey, Arindam, Kumar, Ranjan, Broumi, Said, Bhowmik, Pritam. "Different Types of Operations on Neutrosophic Graphs." International Journal of Neutrosophic Science, vol. Volume 19, no. Issue 2, 2022, pp. 87-94. DOI: https://doi.org/10.54216/IJNS.190208

Dey, A., Kumar, R., Broumi, S., Bhowmik, P. (2022). Different Types of Operations on Neutrosophic Graphs. International Journal of Neutrosophic Science, Volume 19(Issue 2), 87-94. DOI: https://doi.org/10.54216/IJNS.190208

Dey, Arindam, Kumar, Ranjan, Broumi, Said, Bhowmik, Pritam. "Different Types of Operations on Neutrosophic Graphs." International Journal of Neutrosophic Science Volume 19, no. Issue 2 (2022): 87-94. DOI: https://doi.org/10.54216/IJNS.190208

Dey, A., Kumar, R., Broumi, S., Bhowmik, P. (2022) 'Different Types of Operations on Neutrosophic Graphs', International Journal of Neutrosophic Science, Volume 19(Issue 2), pp. 87-94. DOI: https://doi.org/10.54216/IJNS.190208

Dey A, Kumar R, Broumi S, Bhowmik P. Different Types of Operations on Neutrosophic Graphs. International Journal of Neutrosophic Science. 2022;Volume 19(Issue 2):87-94. DOI: https://doi.org/10.54216/IJNS.190208

A. Dey, R. Kumar, S. Broumi, P. Bhowmik, "Different Types of Operations on Neutrosophic Graphs," International Journal of Neutrosophic Science, vol. Volume 19, no. Issue 2, pp. 87-94, 2022. DOI: https://doi.org/10.54216/IJNS.190208

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