Research Article
Open Access
Results on Domination and Chromatic Numbers of Rhombus Silicate Molecular Structure
1
Department of Mathematics, Riphah International University, Faisalabad, Pakistan
2
University Community College, Government College University, Faisalabad, Pakistan
* Corresponding Author:
Haidar Ali,
[email protected]
Volume 1, Issue 2
2025
Received: 13 July 2025
Accepted: 27 July 2025
Published: 15 September 2025
Article Information
Abstract
In this article, we specially focused on rhombus silicate molecular structure. Graph is a data structure for describing complex systems, which contains a set of objects and relationships. A molecular graph, also known as a chemical graph, is a graph-theoretic representation of the structural formula of a chemical compound used in chemical graph theory and mathematical chemistry. A chemical graph is a labelled graph whose edges represent covalent bonds and vertices represent the atoms. A set of vertices (atoms) of a graph G is known as its dominating set with respect to the vertices, if every vertex other than that set is adjacent to some vertex in set. The vertex and edge dominating sets, total domination and chromatic number of rhombus silicate structure has been discussed in this article.
Graphical Abstract
Keywords
domination set $\Upsilon$(G)
domination number with respect to vertices
total domination $\Upsilon_{t}$(G)
edge domination number $\Upsilon^{'}$(G)
chromatic number
rhombus network
Data Availability Statement
Data will be made available on request.
Funding
This work was supported without any funding.
Conflicts of Interest
The authors declare no conflicts of interest.
Ethical Approval and Consent to Participate
Not applicable.
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APA Style
Roman, H., Sohail, A., Rafiq, A., & Ali, H. (2025). Results on Domination and Chromatic Numbers of Rhombus Silicate Molecular Structure. ICCK Journal of Applied Mathematics, 1(2), 86–96. https://doi.org/10.62762/JAM.2025.445811
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TY - JOUR
AU - Roman, Hira
AU - Sohail, Amir
AU - Rafiq, Aneela
AU - Ali, Haidar
PY - 2025
DA - 2025/09/15
TI - Results on Domination and Chromatic Numbers of Rhombus Silicate Molecular Structure
JO - ICCK Journal of Applied Mathematics
T2 - ICCK Journal of Applied Mathematics
JF - ICCK Journal of Applied Mathematics
VL - 1
IS - 2
SP - 86
EP - 96
DO - 10.62762/JAM.2025.445811
UR - https://www.icck.org/article/abs/JAM.2025.445811
KW - domination set $\Upsilon$(G)
KW - domination number with respect to vertices
KW - total domination $\Upsilon_{t}$(G)
KW - edge domination number $\Upsilon^{'}$(G)
KW - chromatic number
KW - rhombus network
AB - In this article, we specially focused on rhombus silicate molecular structure. Graph is a data structure for describing complex systems, which contains a set of objects and relationships. A molecular graph, also known as a chemical graph, is a graph-theoretic representation of the structural formula of a chemical compound used in chemical graph theory and mathematical chemistry. A chemical graph is a labelled graph whose edges represent covalent bonds and vertices represent the atoms. A set of vertices (atoms) of a graph G is known as its dominating set with respect to the vertices, if every vertex other than that set is adjacent to some vertex in set. The vertex and edge dominating sets, total domination and chromatic number of rhombus silicate structure has been discussed in this article.
SN - 3068-5656
PB - Institute of Central Computation and Knowledge
LA - English
ER -
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@article{Roman2025Results,
author = {Hira Roman and Amir Sohail and Aneela Rafiq and Haidar Ali},
title = {Results on Domination and Chromatic Numbers of Rhombus Silicate Molecular Structure},
journal = {ICCK Journal of Applied Mathematics},
year = {2025},
volume = {1},
number = {2},
pages = {86-96},
doi = {10.62762/JAM.2025.445811},
url = {https://www.icck.org/article/abs/JAM.2025.445811},
abstract = {In this article, we specially focused on rhombus silicate molecular structure. Graph is a data structure for describing complex systems, which contains a set of objects and relationships. A molecular graph, also known as a chemical graph, is a graph-theoretic representation of the structural formula of a chemical compound used in chemical graph theory and mathematical chemistry. A chemical graph is a labelled graph whose edges represent covalent bonds and vertices represent the atoms. A set of vertices (atoms) of a graph G is known as its dominating set with respect to the vertices, if every vertex other than that set is adjacent to some vertex in set. The vertex and edge dominating sets, total domination and chromatic number of rhombus silicate structure has been discussed in this article.},
keywords = {domination set \$\Upsilon\$(G), domination number with respect to vertices, total domination \$\Upsilon\_{t}\$(G), edge domination number \$\Upsilon^{'}\$(G), chromatic number, rhombus network},
issn = {3068-5656},
publisher = {Institute of Central Computation and Knowledge}
}
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