Jul 2026· American Journal of Applied Mathematics· 0 citations· 6 references
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.
This thesis investigates two central directions in algebraic graph theory, with an emphasis on spectral methods: spectral determination of graphs and transitivity properties of generalized-Hamming graphs and their complements. The first part focuses on graphs that are determined by the spectra of associated matrices. W...
Let 𝐺 be a 𝑘-regular graph on 𝑛 vertices. In this paper, we determine the maximum and minimum degree energies of two specific graph operations: the extended 𝑚-splitting graph. 𝑆𝑝𝑙𝑚∗ (𝐺) and the 𝑚-semi shadow graph 𝑆𝐷𝑚(𝐺). By applying block matrix decompositions and unitary similarity transformations, we express the max...
Dipakkumar N. Barad, V. Kaneria, K. Popat· International Journal of Mat...· 0 citations
This study explores the spectral characteristics and energy distributions associated with selected graph operations derived from the first Zagreb, second Zagreb, and sum-connectivity matrices to contribute to understanding how algebraic operations induce spectral energy shifts analogous to perturbations in physical or...
S. Sripriya, A. Anuradha· Baghdad Science Journal· 0 citations
Gupta and Iosevich introduced the edge complexity of a graph as the minimum Fourier ratio of its adjacency matrix over all vertex labelings and bounded it below by graph energy divided by the square root of twice the number of edges. We characterize equality for a fixed labeling: the Fourier transform of the adjacency...
Vishal Gupta, A. Iosevich, J. Iosevich et al.· 0 citations
Consider a group [Formula: see text] and construct its power graph, whose vertex set consists of the elements of [Formula: see text]. Two distinct vertices (elements) are adjacent in the graph if and only if one element can be expressed as an integral power of the other. In this article, we improved the bounds of the s...
Priti Prasanna Mondal, Basit A. Mir, Fouzul Atik· Journal of Algebra and its A...· 0 citations
This study establishes exact formulas for the energy, Laplacian energy, and signless Laplacian energy of the lintang graph Ln and its line graph L(Ln). An algebraic spectral framework is employed to construct the associated matrices and determine their eigenvalues explicitly. In contrast to general results on line grap...
F. Fran, Meliana Pasaribu, Helmi Helmi et al.· ZERO Jurnal Sains Matematika...· 0 citations
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