Abstract
Neutrosophicover set (Nover) was introduced by smarandache. Due to some real-time situation, decision-makers deal with uncertainty and inconsistency to identify the best result. Connectivity will be very important in neutrosophic graph. In this research study, we introduced the certain types of domination which are so-called perfect \({\text{NOverTop}}\)-dominating set (perf Noverdom set), connected perfect \({\text{NOverTop}}\)-dominating set (CONN perfNoverdom set), total perfect \({\text{NOverTop}}\)-dominating set (Tot perf Noverdom set), connected total perfect \({\text{NOverTop}}\)-dominating sets (CONN Tot perf Noverdom set), and also properties of domination numbers are established with necessary examples. Further, those relationship are discussed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Revathi, S., P.J. Jayalakshmi, and C.V.R. Harinarayanan. 2013. Perfect dominating sets in fuzzy graphs. IOSR Journal of Mathematics 8 (3): 43–47.
Broumi, S., M. Talea, A. Bakali, and F. Smarandache. 2016. Single valued neutrosophic graphs. Journal of New Theory 10: 86–101.
Smarandache, F., 2016. Neutrosophic over set, neutrosophic under set, neutrosophic off set. Pons Editions, Brussels.
Smarandache, F., 1999. A Unifying Field in Logics: Neutrosophic Logic. American Research Press, pp.1–141.
Somasundaram, A., and S. Somasundaram. 1998. Domination in fuzzy graphs–I. Pattern Recognition Letters 19 (9): 787–791.
Salama, A.A., 2013. Neutrosophic crisp points and neutrosophic crisp ideals. Neutrosophic Sets and Systems 50–53.
Salama, A.A., F. Smarandache, and V. Kroumov. 2014. Neutrosophic crisp sets and neutrosophic crisp topological spaces. Neutrosophic Sets and Systems 25–30.
Salama, A.A., F. Smarandache, and V. Kromov, 2014. Neutrosophic closed set and neutrosophic continuous functions. Neutrosophic Sets and Systems 4–8.
Ore, O., 1962. Theory of graphs. American Mathematical Society Colloquium Publications 38.
Zadeh, L.A., 1965. Fuzzy sets. Information and Control 8 (3): 338–353.
Nagoorgani, A., and V.T. Chandrasekaran, 2006. Domination in fuzzy graph. Advances in Fuzzy Sets and System 17–26.
Revathi, S., C.V.R. Harinarayanan, and R. Muthuraj. 2015. Connected perfect domination in fuzzy graph. Golden Research thoughts 5: 1–5.
Devi, R.N., N. Kalaivani, S. Broumi, and K.A. Venkatesan, 2018. Characterizations of strong and balanced neutrosophic complex graphs. Infinite Study.
Devi, R.N., 2017. Neutrosophic complex N-continuity. Infinite Study.
Devi, R.N., 2020. Minimal domination via neutrosophic over graphs. AIP Conference Proceedings, November 2277: 100019.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Devi, R.N., Muthumari, G., Rasappan, S. (2022). Certain Types of Domination in Nover Top Graphs. In: Peng, SL., Lin, CK., Pal, S. (eds) Proceedings of 2nd International Conference on Mathematical Modeling and Computational Science. Advances in Intelligent Systems and Computing, vol 1422. Springer, Singapore. https://doi.org/10.1007/978-981-19-0182-9_7
Download citation
DOI: https://doi.org/10.1007/978-981-19-0182-9_7
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-19-0181-2
Online ISBN: 978-981-19-0182-9
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)