Mathematics and Computational Sciences

One end node domination of Cartesian product of simple path semigraphs with 1,2 intermediate nodes

Articles in Press

Document Type : Original Article

Authors

D Narmatha 1
R Shakthivel 2
D Veera Vanitha 3
N Nithya Devi 4

1 Department of Mathematics, Sri Ramakrishna Engineering College, Coimbatore

2 Department of Mathematics, Sona College of Technology, Salem

3 Department of Electronics and Communication Engineering, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore.

4 Department of Physical Sciences and Information Technology, Agricultural Engineering College and Research Institute, Tamilnadu Agricultural University, Coimbatore

https://doi.org/10.30511/mcs.2026.2077649.1617
Abstract
Domination concepts in graph theory, have various practical applications in real-world scenarios. In the context of networks, systems, and optimization, domination theory can offer several advantages. In communication or computer networks, domination can be used to optimize the placement of resources such as routers, servers, or communication hubs. A dominating set can represent a minimal number of resources needed to monitor or control the entire network. In this paper, 1e-domination number of the Cartesian product of elementary semigraphs with one and two intermediate nodes are discussed.

Keywords

Semigraph
Path Semigraph
Cartesian Product
1e-Dominating set
1e-Domination number
Subjects
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[3] Jafari, H., Salehfard, S., Aqababaei Dehkordi, D. (2024). Introducing a simple method for detecting the path between two different vertices in the Graphs. Mathematics and Computational Sciences, 4(4), 10-16.
[4] Kamath, S. S., Bhat, R. S. (2003). Domination in semigraphs. Electronic notes in discrete mathematics, 15, 106-111. 
[5] Murugesan, N., Narmatha, D. (2014). Some properties of semigraph and its associated graphs. International Journal of Engineering Research and Technology, 3(5), 898-903. 
[6] Murugesan, N., Narmatha, D. (2019). Dominations In Semigraphs. International Journal of Engineering and Advanced Technology, 8(6), 563-568. 
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Mathematics and Computational Sciences

Articles in Press, Accepted Manuscript
Available Online from 29 May 2026

  • Receive Date 14 November 2025
  • Revise Date 24 May 2026
  • Accept Date 29 May 2026

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