Graph energy is an important concept in spectral graph theory with applications in mathematics and chemistry. In this paper, we study the Laplacian minimum domination energy of derived graphs of some standard graphs. The main aim is to obtain formulas, properties, and bounds for this energy measure. The study considers derived graphs of star graphs, complete bipartite graphs, friendship graphs, and healthy spider graphs. Using minimum dominating sets, minimum domination adjacency matrices, and Laplacian minimum domination matrices, the eigenvalues of these derived graphs are determined. Based on these eigenvalues, explicit formulas for the Laplacian minimum domination energy are obtained. Further, some basic properties related to eigenvalues are established. Upper and lower bounds for the Laplacian minimum domination energy are also derived using matrix methods and classical inequalities such as the Cauchy-Schwarz inequality. The results extend existing work on graph energy by combining domination concepts, Laplacian matrices, and derived graphs. The formulas, properties, and bounds obtained in this paper provide a better understanding of the spectral behavior of derived graphs and may be useful for further research in graph theory and its applications.
| Published in | American Journal of Applied Mathematics (Volume 14, Issue 4) |
| DOI | 10.11648/j.ajam.20261404.14 |
| Page(s) | 210-219 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2026. Published by Science Publishing Group |
Laplacian Minimum Domination Derived Matrix, Laplacian Minimum Domination Derived Eigenvalues, Laplacian Minimum Domination Energy
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APA Style
Rajanna, J., Shashidhara, A. A. (2026). Laplacian Minimum Domination Energy of Some Derived Graphs. American Journal of Applied Mathematics, 14(4), 210-219. https://doi.org/10.11648/j.ajam.20261404.14
ACS Style
Rajanna, J.; Shashidhara, A. A. Laplacian Minimum Domination Energy of Some Derived Graphs. Am. J. Appl. Math. 2026, 14(4), 210-219. doi: 10.11648/j.ajam.20261404.14
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Download@article{10.11648/j.ajam.20261404.14,
author = {Jagadeesh Rajanna and Ashwini Ankanahalli Shashidhara},
title = {Laplacian Minimum Domination Energy of Some Derived Graphs},
journal = {American Journal of Applied Mathematics},
volume = {14},
number = {4},
pages = {210-219},
doi = {10.11648/j.ajam.20261404.14},
url = {https://doi.org/10.11648/j.ajam.20261404.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20261404.14},
abstract = {Graph energy is an important concept in spectral graph theory with applications in mathematics and chemistry. In this paper, we study the Laplacian minimum domination energy of derived graphs of some standard graphs. The main aim is to obtain formulas, properties, and bounds for this energy measure. The study considers derived graphs of star graphs, complete bipartite graphs, friendship graphs, and healthy spider graphs. Using minimum dominating sets, minimum domination adjacency matrices, and Laplacian minimum domination matrices, the eigenvalues of these derived graphs are determined. Based on these eigenvalues, explicit formulas for the Laplacian minimum domination energy are obtained. Further, some basic properties related to eigenvalues are established. Upper and lower bounds for the Laplacian minimum domination energy are also derived using matrix methods and classical inequalities such as the Cauchy-Schwarz inequality. The results extend existing work on graph energy by combining domination concepts, Laplacian matrices, and derived graphs. The formulas, properties, and bounds obtained in this paper provide a better understanding of the spectral behavior of derived graphs and may be useful for further research in graph theory and its applications.},
year = {2026}
}
TY - JOUR T1 - Laplacian Minimum Domination Energy of Some Derived Graphs AU - Jagadeesh Rajanna AU - Ashwini Ankanahalli Shashidhara Y1 - 2026/07/17 PY - 2026 N1 - https://doi.org/10.11648/j.ajam.20261404.14 DO - 10.11648/j.ajam.20261404.14 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 210 EP - 219 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20261404.14 AB - Graph energy is an important concept in spectral graph theory with applications in mathematics and chemistry. In this paper, we study the Laplacian minimum domination energy of derived graphs of some standard graphs. The main aim is to obtain formulas, properties, and bounds for this energy measure. The study considers derived graphs of star graphs, complete bipartite graphs, friendship graphs, and healthy spider graphs. Using minimum dominating sets, minimum domination adjacency matrices, and Laplacian minimum domination matrices, the eigenvalues of these derived graphs are determined. Based on these eigenvalues, explicit formulas for the Laplacian minimum domination energy are obtained. Further, some basic properties related to eigenvalues are established. Upper and lower bounds for the Laplacian minimum domination energy are also derived using matrix methods and classical inequalities such as the Cauchy-Schwarz inequality. The results extend existing work on graph energy by combining domination concepts, Laplacian matrices, and derived graphs. The formulas, properties, and bounds obtained in this paper provide a better understanding of the spectral behavior of derived graphs and may be useful for further research in graph theory and its applications. VL - 14 IS - 4 ER -
Department of Mathematics, Government First Grade College, Banglore University, Channapatna, India
Department of Mathematics, PG Centre Ramanagara, Banglore University, Bangore South, India
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