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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SAFE DOMINATION IN THE LADDER GRAPH

Authors

  • Marsha Ella L. Maceren
  • Isagani S. Cabahug, Jr.

Keywords:

safe dominating set, ladder graph

DOI:

https://doi.org/10.17654/0974165824024

Abstract

Let $G$ be a simple connected graph. A nonempty subset $S \subseteq V(G)$ is a safe dominating set if $S$ is a dominating set of $G$ and for every component $A$ of $G[S]$ and every component $B$ of $G[V(G) \backslash S]$ adjacent to $A,|A| \geq|B|$. A safe dominating set of the smallest size in a given graph is called the safe domination set denoted as $\gamma_s$-set. The cardinality of $\gamma_s$-set is called safe domination number. In this paper, we determine sufficient conditions for the safe dominating set of a ladder graph. Moreover, we provide the upper bound of the safe domination number of such a graph.

Received: March 6, 2024
Accepted: May 1, 2024

References

O. J. Adeleke and D. O. Olukanni, Facility location problems: models, techniques, and applications in waste management, Recycling 5(2) (2020), 10. https://doi.org/10.3390/recycling5020010.

Isagani S. Cabahug Jr. et al., Introducing safe domination in graphs, International Journal of Mathematics Trends and Technology 69(10) (2023).

https://doi.org/10.14445/22315373/IJMTT-V69I10P503.

S. Fujita, G. MacGillivray and T. Sakuma, Safe set problem on graphs, Discrete Appl. Math. 215 (2016), 106-111. https://dx.doi.org/10.1016/j.dam.2016.07.020.

Kyle Kenneth Ruaya, Isagani S. Cabahug, Jr. and Rolito Eballe, Another look of rings domination in ladder graph, Asian Research Journal of Mathematics 18 (2022), 27-33. 10.9734/ARJOM/2022/v18i12622.

K. S. R. Tan and I. S. Cabahug, Jr., Safe sets in some graph families, Asian Research Journal of Mathematics 18(9) (2021), 1-5.

https://doi.org/10.9734/ARJOM/2022/v18i930399.

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Published

2024-05-11

Issue

Vol. 41 No. 4 (2024)

Section

Articles

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Copyright (c) 2024 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA

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

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How to Cite

SAFE DOMINATION IN THE LADDER GRAPH. (2024). Advances and Applications in Discrete Mathematics, 41(4), 331-339. https://doi.org/10.17654/0974165824024

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