آمار
| تعداد نشریات | 5 |
| تعداد شماره‌ها | 116 |
| تعداد مقالات | 1,355 |
| تعداد مشاهده مقاله | 1,361,280 |
| تعداد دریافت فایل اصل مقاله | 1,313,795 |
Remarks on the Bounds of Graph Energy | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 تیر 1403 اصل مقاله (421.93 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.28825.1739 | ||
| نویسندگان | ||
| Ş. Burcu Bozkurt Altındağ* 1؛ Emina Milovanović2؛ Marjan Matejić2؛ Igor Milovanović2 | ||
| 1Selçuk University | ||
| 2University of Niš, Faculty of Electronic Engineering, Niš, Serbia | ||
| چکیده | ||
| Let $G$ be a graph of order $n$ with eigenvalues $\lambda _{1}\geq \lambda_{2}\geq \cdots \geq \lambda _{n}.$ The energy of $G$ is defined as $E\left(G\right) =\sum_{i=1}^{n}\left\vert \lambda _{i}\right\vert $. In the present paper, new bounds on $E(G)$ are provided. In addition, some bounds of $E(G)$ are compared. | ||
| کلیدواژه‌ها | ||
| Graph spectra؛ graph invariants؛ energy of graph | ||
| مراجع | ||
|
[1] S. Akbari, A. Alazemi, M. Anđelić, and M.A. Hosseinzadeh, On the energy of line graphs, Linear Algebra Appl. 636 (2022), 143–153. https://doi.org/10.1016/j.laa.2021.11.022 [2] S. Akbari, M. Ghahremani, M.A. Hosseinzadeh, S.K. Ghezelahmad, H. Rasouli, and A. Tehranian, A lower bound for graph energy in terms of minimum and maximum degrees, MATCH Commun. Math. Comput. Chem. 86 (2021), 549– 558. [3] S. Akbari and M.A. Hosseinzadeh, A short proof for graph energy is at least twice of minimum degree, MATCH Commun. Math. Comput. Chem. 83 (2020), 631–633.
[4] S. Al-Yakooba, S. Filipovskib, and D. Stevanović, Proofs of a few special cases of a conjecture on energy of non-ingular graphs, MATCH Commun. Math. Comput. Chem. 86 (2021), 577–586.
[5] Ş.B.B. Altındağ and D. Bozkurt, Lower bounds for the energy of (bipartite) graphs, MATCH Commun. Math. Comput. Chem. 77 (2017), 9–14.
[6] G. Caporossi, D. Cvetković, I. Gutman, and P. Hansen, Variable neighborhood search for extremal graphs. 2. Finding graphs with extremal energy, J. Chem. Inf. Comput. 39 (1999), no. 6, 984–996. https://doi.org/10.1021/ci9801419 [7] V. Cirtoaje, The best lower bound depended on two fixed variables for Jensen’s inequality with ordered variables, J. Inequal. Appl. 2010 (2010), Article number: 128258. https://doi.org/10.1155/2010/128258 [8] D.M. Cvetković, M. Doob, and H. Sachs, Spectra of Graphs: Theory and Application, Academic Press, New York, 1980.
[9] K.C. Das and S. Elumalai, On energy of graphs, MATCH Commun. Math. Comput. Chem. 77 (2017), no. 1, 3–8.
[10] K.C. Das, I. Gutman, I. Milovanović, E. Milovanović, and B. Furtula, Degree-based energies of graphs, Linear Algebra Appl. 554 (2018), 185–204. https://doi.org/10.1016/j.laa.2018.05.027 [11] K.C. Das, S.A. Mojallal, and I. Gutman, Relations between degrees, conjugate degrees and graph energies, Linear Algebra Appl. 515 (2017), 24–37. https://doi.org/10.1016/j.laa.2016.11.009 [12] G.H. Fath-Tabar and A.R. Ashrafi, Some remarks on Laplacian eigenvalues and Laplacian energy of graphs, Math. Commun. 15 (2010), no. 2, 443–451.
[13] O. Favaron, M. Mahéo, and J.F. Saclé, Some eigenvalue properties in graphs (conjectures of Graffiti—II), Discrete Math. 111 (1993), no. 1-3, 197–220. https://doi.org/10.1016/0012-365X(93)90156-N [14] S. Filipovski, New bounds for the first Zagreb index, MATCH Commun. Math. Comput. Chem. 85 (2021), no. 2, 303–312.
[15] S. Filipovski, Relations between the energy of graphs and other graph parameters, MATCH Commun. Math. Comput. Chem. 87 (2022), 661–672.
[16] S. Filipovski and R. Jajcay, New upper bounds for the energy and spectral radius of graphs, MATCH Commun. Math. Comput. Chem. 84 (2020), 335–343.
[17] S. Filipovski and R. Jajcay, Bounds for the energy of graphs, Mathematics 9 (2021), no. 14, Article ID: 1687. https://doi.org/10.3390/math9141687 [18] S. Furuichi, On refined Young inequalities and reverse inequalities, J. Math. Inequal. 5 (2011), no. 1, 21–31.
[19] I. Gutman, The energy of a graph, Ber. Math. Statist. Sekt. Forschungsz. Graz 103 (1978), 1–22.
[20] I. Gutman, Oboudi-type bounds for graph energy, Math. Interdisc. Res. 4 (2019), no. 2, 151–155. https://doi.org/10.22052/mir.2019.207442.1172 [21] I. Gutman and B. Furtula, Recent Results in the Theory of Randić Index, (Eds.), University of Kragujevac and Faculty of Science Kragujevac, 2008.
[22] P. Henrici, Two remarks on the Kantorovich inequality, Am. Math. Mon. 68 (1961), no. 9, 904–906. https://doi.org/10.2307/2311698 [23] X. Li, Y. Shi, and I. Gutman, Graph Energy, Springer, New York, 2012.
[24] B.J. McClelland, Properties of the latent roots of a matrix: the estimation of π-electron energies, J. Chem. Phys. 54 (1971), no. 2, 640–643. https://doi.org/10.1063/1.1674889 [25] I.Ž. Milovanović, E.I. Milovanović, M.M. Matejić, and A. Ali, A note on the relationship between graph energy and determinant of adjacency matrix, Discrete Math. Algorithms Appl. 11 (2019), no. 1, Article ID: 1950001. https://doi.org/10.1142/S1793830919500010 [26] I.Ž. Milovanović, E.I. Milovanović, and A. Zakić, A short note on graph energy, MATCH Commun. Math. Comput. Chem. 72 (2014), 179–182.
[27] I.Ž. Milovanović, V.M. Ciric, and E.I. Milovanović, On some spectral, vertex and edge degree–based graph invariants, MATCH Commun. Math. Comput. Chem. 77 (2017), 177–188.
[28] D. S. Mitrinović and P. M. Vasić, Analytic Inequalities, Springer Berlin, Heidelberg, 2012.
[29] D.S. Mitrinović, J. Pečarić, and A.M. Fink, Classical and New Inequalities in Analysis, Springer Dordrecht, 2013.
[30] M.R. Oboudi, A new lower bound for the energy of graphs, Linear Algebra Appl. 580 (2019), 384–395. https://doi.org/10.1016/j.laa.2019.06.026 [31] M. Randić, Characterization of molecular branching, J. Am. Chem. Soc. 97 (1975), no. 23, 6609–6615. https://doi.org/10.1021/ja00856a001 [32] B.C. Rennie, On a class of inequalities, J. Aust. Math. Soc. 3 (1963), no. 4, 442–448.
[33] Z. Yan, X. Zheng, and J. Li, Some degree-based topological indices and (normalized Laplacian) energy of graphs, Discrete Math. Lett. 11 (2023), 19–26. https://doi.org/10.47443/dml.2022.059 | ||
|
آمار تعداد مشاهده مقاله: 263 تعداد دریافت فایل اصل مقاله: 585 |
||