Proper d-Lucky Number for Certain Rooted Product Graphs

Chiranjilal Kujur

doi:10.17485/IJST/v16i4.2146

Article

Proper d-Lucky Number for Certain Rooted Product Graphs

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i4.2146

Year: 2023, Volume: 16, Issue: 4, Pages: 249-253

Original Article

Proper d-Lucky Number for Certain Rooted Product Graphs

Chiranjilal Kujur^1*

¹Assistant Professor, St. Joseph’s College, Darjeeling, 734426, West Bengal, India

*Corresponding Author
Email: [email protected]

Received Date:07 November 2022, Accepted Date:22 December 2022, Published Date:27 January 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: In this study, rooted product of path with cycle, path with complete graph cycle with complete graph and complete graph with complete graphs are taken and examined for the existence of d-lucky labeling for the same. Methods: The rooted product graphs are obtained of path with cycle, path with complete graph, cycle with complete graph and complete graph with itself and then proper d-lucky numbers are obtained for the above mentioned graphs. Construction and descriptive method are used to prove the results. Findings: Proper d-lucky labeling for the said graphs are verified and proper d-lucky numbers for the same are obtained. Novelty: It involves the mathematical formulations which involves labeling the vertices of a graph in such a manner that no two adjacent vertices have the same labeling and the neighborhood sums and degree sums of the adjacent vertices are different, which gives rise to proper d-lucky labeling.

Keywords: d-Lucky Labeling; d-Lucky Numbers; Proper d-Lucky Labeling; Proper d-Lucky Number; Rooted Product

References

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Copyright

© 2023 Kujur. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)