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On the reciprocal distance Laplacian spectral radius of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 21 تیر 1403 اصل مقاله (396.17 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29493.2024 | ||
| نویسندگان | ||
| Ummer Mushtaq؛ Shariefuddin Pirzada* | ||
| Department of Mathematics, University of Kashmir, Srinagar, India | ||
| چکیده | ||
| The reciprocal distance Laplacian matrix of a connected graph $G$ is defined as $RD^L(G)=RTr(G)-RD(G)$, where $RTr(G)$ is the diagonal matrix whose $i$-th element $RTr(v_i)=\sum_{i\ne j\in V(G)} \frac{1}{d_{ij}}$ and $RD(G)$ is the Harary matrix. $RD^L(G)$ is a real symmetric matrix and we denote its eigenvalues as $\lambda_1(RD^L(G))\geq \lambda_2(RD^L(G))\geq\dots\geq\lambda_n(RD^L(G))$. The largest eigenvalue $\lambda_1(RD^L(G))$ of $RD^L(G)$ is called the reciprocal distance Laplacian spectral radius. In this paper, we obtain upper bounds for the reciprocal distance Laplacian spectral radius. We characterize the extremal graphs attaining this bound. | ||
| کلیدواژه‌ها | ||
| Distance Laplacian matrix؛ reciprocal distance Laplacian matrix؛ Harary index؛ reciprocal distance Laplacian eigenvalues؛ reciprocal distance Laplacian spectral radius | ||
| مراجع | ||
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[5] 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. https://doi.org/10.2298/FIL2323973P [6] D. Plavšić, S. Nikolić, N. Trinajstić, and Z. Mihalić, On the Harary index for the characterization of chemical graphs, J. Math. Chem. 12 (1993), no. 1, 235–250. https://doi.org/10.1007/BF01164638 [7] W. So, Commutativity and spectra of Hermitian matrices, Linear Algebra Appl. 212–213 (1994), 121–129. https://doi.org/10.1016/0024-3795(94)90399-9 [8] L. You, M. Yang, W. So, and W. Xi, On the spectrum of an equitable quotient matrix and its application, Linear Algebra Appl. 577 (2019), 21–40. https://doi.org/10.1016/j.laa.2019.04.013 | ||
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