Advances and Applications in Discrete Mathematics

The Advances and Applications in Discrete Mathematics is a prestigious peer-reviewed journal indexed in the Emerging Sources Citation Index (ESCI). It is dedicated to publishing original research articles in the field of discrete mathematics and combinatorics, including topics such as graphs, coding theory, and block design. The journal emphasizes efficient and powerful tools for real-world applications and welcomes expository articles that highlight current developments in the field.

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SECURE VERTEX COVER PEBBLING NUMBER FOR FAMILIES OF TREE-DERIVED STRUCTURES

Authors

  • S. Sarah Surya
  • Lian Mathew
  • Jyothy Thomas
  • Jeet Kurian Mattam

Keywords:

pebbling, secure vertex cover, secure vertex cover pebbling number

DOI:

https://doi.org/10.17654/0974165825012

Abstract

The secure vertex cover pebbling number of a graph $G$, is the smallest number $m$ that allows every distribution of $m$ pebbles to reach some secure vertex cover of $G$ by a sequence of pebbling moves. Trees are advantageous in biological science especially in systematics, bioinformatics and phylogenetics. In this paper, the secure vertex cover pebbling number for some tree-derived structures such as coconut tree, comb graph, Bistar graph, Banana tree and complete binary tree has been determined.

Received: July 27, 2024
Revised: August 15, 2024
Accepted: November 15, 2024

References

F. R. K. Chung, Pebbling in hypercubes, SIAM Journal on Discrete Mathematics 2(4) (1989), 467-472.

G. H. Hurlbert, A survey of graph pebbling, In Congr. Numer. 139 (1999), 41-64.

Glenn H. Hurlbert, Lian Mathew, Jasintha Quadras and S. Sarah Surya, On secure vertex cover pebbling number, Asian-European Journal of Mathematics 16(10) (2023), 1-16.

R. Prabha and S. Renuka Devi, General position problem of hyper tree and shuffle hyper tree networks, AIP Conference Proceedings, No. 1. AIP Publishing LLC, 2020.

S. Sarah Surya, Alan Thomas and Lian Mathew, Integer cordial labeling of some families of graphs, Ratio Mathematica 42 (2022), 105-114.

S. Sarah Surya and Lian Mathew, Bound for secure vertex cover pebbling number for hypercube, Proyoccenies Journal of Mathematics, under review.

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Published

2024-12-31

Issue

Vol. 42 No. 2 (2025)

Section

Articles

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How to Cite

SECURE VERTEX COVER PEBBLING NUMBER FOR FAMILIES OF TREE-DERIVED STRUCTURES. (2024). Advances and Applications in Discrete Mathematics, 42(2), 177-190. https://doi.org/10.17654/0974165825012

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