آمار
| تعداد نشریات | 6 |
| تعداد شمارهها | 125 |
| تعداد مقالات | 1,585 |
| تعداد مشاهده مقاله | 1,753,075 |
| تعداد دریافت فایل اصل مقاله | 1,634,888 |
On the reciprocal distance Laplacian spectral radius of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 19، دوره 11، شماره 1، خرداد 2026، صفحه 259-268 اصل مقاله (396.48 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 | ||
|
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] 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
[4] S. Pirzada, An Introduction to Graph Theory, Universities Press, 2012.
[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 | ||
|
آمار تعداد مشاهده مقاله: 384 تعداد دریافت فایل اصل مقاله: 739 |
||