A Study on Edge Pebbling Number, Covering Cover Edge Pebbling Number of Friendship Graphs, Odd Path and Even Path

Priscilla Paul; S Syed Ali Fathima

doi:10.17485/IJST/v16i32.674

Article

A Study on Edge Pebbling Number, Covering Cover Edge Pebbling Number of Friendship Graphs, Odd Path and Even Path

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i32.674

Year: 2023, Volume: 16, Issue: 32, Pages: 2480-2484

Original Article

A Study on Edge Pebbling Number, Covering Cover Edge Pebbling Number of Friendship Graphs, Odd Path and Even Path

Priscilla Paul^1,2*, S Syed Ali Fathima³

¹Research Scholar, Reg. No. 18131282092016, Department of Mathematics, Sadakathullah Appa College (Autonomous), Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Rahmath Nagar, 627011, Tirunelveli
²Assistant Professor, Department of Mathematics, Lady Doak College (Autonomous), Madurai
³Assistant Professor of Mathematics, Sadakathullah Appa College (Autonomous), Rahmath Nagar, Tirunelveli, 627011

*Corresponding Author
Email: [email protected]

Received Date:25 March 2023, Accepted Date:17 July 2023, Published Date:21 August 2023

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

Abstract

Objectives: To find the edge pebbling number and covering cover edge pebbling number of friendship graphs. Methods: The possible minimum edge covering set of the friendship graph is considered and the set with the minimum pebble requirement covering all vertices is selected. Findings: Obtained the modified result of edge pebbling number of friendship graph, defined the covering cover edge pebbling number of a graph G, and covering cover edge pebbling number for friendship graphs, odd path and even path is found. Also found that friendship graphs are edge demonic. Novelty: Finding the covering cover edge pebbling number of a graph plays a vital role in optimization problems. Since all the vertices are covered, for instance the locations of mobile towers can be considered as edges and residential areas as vertices, and network signals can be modified according to the number of pebbles.

Keywords: Friendship Graphs; Odd Path; Even Path; Minimum Edge Covering Set; Edge Pebbling Number; Edge Demonic; Covering Cover Edge Pebbling Number

References

Paul P, A. On Edge Pebbling number and Cover Edge Pebbling number of some graphs. Journal of Information and Computational Science. 2020;10(6):337–381. Available from: https://doi.org/10.12733.jics.2020.v10i6.535569.12540
Priscilla AP, Fathima SSA. On Cover Edge Pebbling Number of Helm Graph, Crown Graph and Pan Graph. European Chemical Bulletin. 2023;12(3):873–879. Available from: https://www.eurchembull.com/uploads/paper/1c2e674b9fbf5b0bcad44d79c1d67a5c.pdf
Priscilla AP, Fathima SSA. A New Approach on Finding the Edge Pebbling Number of Edge Demonic Graphs. Journal of Xidian University. 2022;16(3):178–180. Available from: https://doi.org/10.37896/jxu16.3/019

Copyright

© 2023 Paul & Fathima. 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)