آمار
| تعداد نشریات | 5 |
| تعداد شماره‌ها | 111 |
| تعداد مقالات | 1,247 |
| تعداد مشاهده مقاله | 1,199,883 |
| تعداد دریافت فایل اصل مقاله | 1,060,656 |
Maximizing the indices of a class of signed complete graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 14، دوره 9، شماره 1، خرداد 2024، صفحه 169-175 اصل مقاله (358.31 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2022.28103.1442 | ||
| نویسندگان | ||
| Navid Kafai؛ Farideh Heydari* | ||
| Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran | ||
| چکیده | ||
| The index of a signed graph is the largest eigenvalue of its adjacency matrix. Let $\mathfrak{U}_{n,k,4}$ be the set of all signed complete graphs of order $n$ whose negative edges induce a unicyclic graph of order $k$ and girth at least $4$. In this paper, we identify the signed graphs achieving the maximum index in the class $\mathfrak{U}_{n,k,4}$. | ||
| کلیدواژه‌ها | ||
| Index؛ Signed complete graph؛ Unicyclic | ||
| مراجع | ||
|
[1] S. Akbari, F. Belardo, F. Heydari, M. Maghasedi, and M. Souri, On the largest eigenvalue of signed unicyclic graphs, Linear Algebra Appl. 581 (2019), 145–162. https://doi.org/10.1016/j.laa.2019.06.016
[2] S. Akbari, S. Dalvandi, F. Heydari, and M. Maghasedi, Signed complete graphs with maximum index., Discuss. Math. Graph Theory 40 (2020), no. 2, 393–403. http://dx.doi.org/10.7151/dmgt.2276
[3] F. Belardo, M. Brunetti, M. Cavaleri, and A. Donno, Constructing cospectral signed graphs, Linear Multilinear Algebra 69 (2021), no. 14, 2717–2732. https://doi.org/10.1080/03081087.2019.1694483
[4] M. Brunetti and A. Ciampella, Signed bicyclic graphs with minimal index, Commun. Comb. Optim. 8 (2023), no. 1, 207–241. https://doi.org/10.22049/cco.2022.27346.1241
[5] M. Brunetti and Z. Stanić, Ordering signed graphs with large index, Ars Math. Contemp. 22 (2022), no. 4, #P4.05. https://doi.org/10.26493/1855-3974.2714.9b3
[6] M. Brunetti and Z. Stanić, Unbalanced signed graphs with extremal spectral radius or index, Comput. Appl. Math. 41 (2022), no. 3, 1–13. https://doi.org/10.1007/s40314-022-01814-5
[7] D.M. Cvetković, P. Rowlinson, and S. Simi´c, An Introduction to the Theory of Graph Spectra, Cambridge University Press, Cambridge, 2010.
[8] N. Kafai, F. Heydari, N. Jafari Rad, and M. Maghasedi, On the signed complete graphs with maximum index, Iran. J. Sci. Technol. Trans. A Sci. 45 (2021), no. 6, 2085–2090. https://doi.org/10.1007/s40995-021-01199-w
[9] T. Koledin and Z. Stanić, Connected signed graphs of fixed order, size, and number of negative edges with maximal index, Linear Multilinear Algebra 65 (2017), no. 11, 2187–2198. https://doi.org/10.1080/03081087.2016.1265480
[10] T.V. Shijin, P. Soorya, K. Shahul Hameed, and K.A. Germina, On the distance spectra of product of signed graphs, Commun. Comb. Optim. 8 (2023), no. 1, 67–76. https://doi.org/10.22049/cco.2021.27304.1227
[11] Z. Stanić, Integral regular net-balanced signed graphs with vertex degree at most four., Ars Math. Contemp. 17 (2019), no. 1, 103–114. https://doi.org/10.26493/1855-3974.1740.803
[12] T. Zaslavsky, Matrices in the theory of signed simple graphs, Advances in Discrete Mathematics and Applications, Ramanujan Mathematical Society Lecture Notes Series 13, Ramanujan Mathematical Society, Mysore, 2010, pp. 207–229. | ||
|
آمار تعداد مشاهده مقاله: 374 تعداد دریافت فایل اصل مقاله: 1,181 |
||