Reciprocal distance Laplacian spectral radius of graphs

Ahmad, Hilal; Rather, Bilal Ahmad; Shang, Yilun

doi:10.22049/cco.2025.29137.1857

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	Reciprocal distance Laplacian spectral radius of graphs
Communications in Combinatorics and Optimization
مقاله 16، دوره 12، شماره 1، خرداد 2027، صفحه 247-262 اصل مقاله (460.68 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2025.29137.1857
نویسندگان
Hilal Ahmad^* ¹؛ Bilal Ahmad Rather²؛ Yilun Shang³
¹Department of School Education JK Govt. Kashmir, India
²Department of Mathematics, Smarkand International University of Technology, Samarkand 140100, Uzbekistan
³Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK
چکیده
For a simple connected graph $ G $ with $ V(G)=\{v_{1},v_{2},\dots,v_{n}\} $, let $ d_{ij} $ be the distance between any pair of distinct vertices $ v_{j} $ and $ v_{j}. $ The reciprocal distance Laplacian matrix $ RD^{L}(G) $ of $ G $ is defined by $ RD^{L}(G)=RTr(G)-RD(G) $, where $ RTr(G) $ is the diagonal matrix having $ i $-the entry $ RTr(v_{i})=\sum_{j\in V(G)}\frac{1}{d_{ij}} $ and $ RD(G) $ is the reciprocal distance matrix (also called Harary matrix) having $ (i,j) $-th entry $ \frac{1}{d_{ij}} $ if $ i\neq j $ and zero, otherwise. The set of all $ RD^{L}(G) $-eigenvalues $ \delta_{1}\geq \delta_{2}\geq \dots\geq \delta_{n-1}>\delta_{n} $ is known as the $ RD^{L} $-spectrum (also called reciprocal distance Laplacian spectrum) of $ G $ and $ \delta_{1} $ is called the $ RD^{L}$-spectral radius (also called reciprocal distance Laplacian spectral radius) of $ G. $ We explore various interesting properties of $ RD^{L} $-eigenvalues along with the bounds for $ RD^{L} $-spectral radius. We characterize the corresponding extremal graphs attaining these bounds.
کلیدواژه‌ها
distance matrix؛ distance Laplacian matrix؛ reciprocal distance Laplacian matrix؛ largest eigenvalue

مراجع
[1] M. Andelic, S. Khan, and S. Pirzada, On graphs with a few distinct reciprocal distance Laplacian eigenvalues, AIMS Math. 8 (2023), no. 12, 29008–29016. https://doi.org/10.3934/math.20231485 [2] M. Aouchiche and P. Hansen, Two Laplacians for the distance matrix of a graph, Linear Algebra Appl. 439 (2013), no. 1, 21–33. https://doi.org/10.1016/j.laa.2013.02.030 [3] M. Aouchiche and P. Hansen, Distance spectra of graphs: A survey, Linear Algebra Appl. 458 (2014), 301–386. https://doi.org/10.1016/j.laa.2014.06.010 [4] R. Bapat and S.K. Panda, The spectral radius of the reciprocal distance Laplacian matrix of a graph, Bull. Iranian Math. Soc. 44 (2018), no. 5, 1211–1216. https://doi.org/10.1007/s41980-018-0084-z [5] G. Chartrand and P. Zhang, Introductory Graph Theory, Tata McGraw-Hill edition, New Delhi, 2006. [6] Z. Cui and B. Liu, On Harary matrix, Harary index and Harary energy, MATCH Commun. Math. Comput. Chem. 68 (2012), no. 3, 815–823. [7] C. Cvetković, R. Peter, and S. Slobodan, An Introduction to the Theory of Graph Spectra, Cambridge University Press, 2009. [8] H.A. Ganie, B.A. Rather, and M. Aouchiche, Reciprocal distance Laplacian spectral properties double stars and their complements, Carpathian Math. Publ. 15 (2023), no. 2, 576–593. https://doi.org/10.15330/cmp.15.2.576-593 [9] L. Huiqiu, S. Jinlong, X. Jie, and Z. Yuke, A survey on distance spectra of graphs, Adv. Math. 50 (2021), no. 1, 29–76. [10] S. Khan, S. Pirzada, and Y. Shang, On the sum and spread of reciprocal distance Laplacian eigenvalues of graphs in terms of harary index, Symmetry 14 (2022), no. 9, 1937. https://doi.org/10.3390/sym14091937 [11] A. Lupa¸s, Inequalities for the roots of a class of polynomials, Publ. Elektroteh. Fak., Univ. Beogradu, Ser. (1977), no. 577/598, 79–85. [12] L. Medina and M. Trigo, Upper bounds and lower bounds for the spectral radius of reciprocal distance, reciprocal distance Laplacian and reciprocal distance signless laplacian matrices, Linear Algebra Appl. 609 (2021), 386–412. https://doi.org/10.1016/j.laa.2020.09.024 [13] L. Medina and M. Trigo, Bounds on the reciprocal distance energy and reciprocal distance Laplacian energies of a graph, Linear Multilinear Algebra 70 (2022), no. 16, 3097–3118. https://doi.org/10.1080/03081087.2020.1825607 [14] S. Pirzada and S. Khan, On the distribution of eigenvalues of the reciprocal distance Laplacian matrix of graphs, Filomat 37 (2023), no. 23, 7973–7980. [15] O. Rojo and H. Rojo, A decreasing sequence of upper bounds on the largest Laplacian eigenvalue of a graph, Linear Algebra Appl. 381 (2004), 97–116. https://doi.org/10.1016/j.laa.2003.10.026 [16] R. Sharafdini and A.Z. Abdian, Tarantula graphs are determined by their Laplacian spectrum, Electron. J. Graph Theory Appl. 9 (2021), no. 2, 419–432. https://doi.org/10.5614/ejgta.2021.9.2.14 [17] B. Zhou and N. Trinajstić, Maximum eigenvalues of the reciprocal distance matrix and the reverse Wiener matrix, Int. J. Quantum Chem. 108 (2008), no. 5, 858–864. https://doi.org/10.1002/qua.21558
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Reciprocal distance Laplacian spectral radius of graphs