پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 673 |
| تعداد مقالات | 9,831 |
| تعداد مشاهده مقاله | 69,796,491 |
| تعداد دریافت فایل اصل مقاله | 49,161,028 |
New bound for edge spectral radius and edge energy of graphs | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 100، دوره 13، شماره 1، خرداد 2022، صفحه 1175-1181 اصل مقاله (315.72 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23361.2523 | ||
| نویسندگان | ||
| Saeed Mohammadian Semnani؛ Samira Sabeti* | ||
| Department of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran. | ||
| تاریخ دریافت: 18 اردیبهشت 1400، تاریخ پذیرش: 05 مهر 1400 | ||
| چکیده | ||
| Let $ X(V,E) $ be a simple graph with $ n $ vertices and $ m $ edges without isolated vertices. Denote by $ B = (b_{ij})_{m\times m} $ the edge adjacency matrix of $ X $. Eigenvalues of the matrix $ B $, $\mu_1, \mu_2, \cdots, \mu_m $, are the edge spectrum of the graph $ X $. An important edge spectrum-based invariant is the graph energy, defined as $ E_e(X) =\sum_{i=1}^{m} \vert \mu_i \vert $. Suppose $ B^{'} $ be an edge subset of $ E(X) $ (set of edges of $ X $). For any $ e \in B^{'} $ the degree of the edge $ e_i $ with respect to the subset $ B^{'} $ is defined as the number of edges in $ B^{'} $ that are adjacent to $ e_i $. We call it as $ \varepsilon $-degree and is denoted by $ \varepsilon_i $. Denote $ \mu_1(X) $ as the largest eigenvalue of the graph $ X $ and $ s_i $ as the sum of $ \varepsilon $-degree of edges that are adjacent to $ e_i $. In this paper, we give lower bounds of $ \mu_1(X) $ and $ \mu_1^{D^{'}}(X) $ in terms of $ \varepsilon $-degree. Consequently, some existing bounds on the graph invariants $ E_e(X) $ are improved. | ||
| کلیدواژهها | ||
| ε-degree؛ adjacency matrix؛ spectral radius؛ dominating set؛ graph energy؛ bound of energy | ||
| مراجع | ||
|
[1] S. Arumugam and S. Velammal, Edge domination in graphs, Taiwanese J. Math., 2(2) (1998) 173-179. 2] M. H. Akhbari, K. K. Choong and F. Movahedi, A note on the minimum edge dominating energy of graphs, J. Appl. Math. Comput., 63(1) (2020) 295-310. [3] R. B. Bapat, Graphs and Matrices, Hindustan Book Agency, 2011. [4] D. Cvetkovi´c, M. Doob and H. Sachs, Spectra of Graphs-Theory and Application, Academic Press, New York, 1980; 2nd revised ed.: Barth, Heidelberg, 1995. [5] D. Cvetkovic, P. Rowlinson and S. Simic, An Introduction to the Theory of Graph Spectra, Cambridge Univ. Press, Cambridge, 2010. [6] E. Estrada and A. Ramırez, Edge adjacency relationships and molecular topographic descriptors. Definition and QSAR applications, J. Chem. Inf. Comput. Sci. , 36(4)(1996) 837-843. [7] A. D. G¨ung¨or and S. B. Bozkurt, On the distance spectral radius and the distance energy of graphs, Linear Multilinear Algebra, 59(4)(2011) 365-370. [8] I. Gutman, Total π-electron energy of benzenoid hydrocarbons, Topics Curr. Chem., 162(1992) 29-63. [9] A. Jahanbani, Lower bounds for the energy of graphs, AKCE Int. J. Graphs Comb., 18(1)(2018) 88-96, https://doi.org/10.1016/j.akcej.2017.10.007. [10] V. Nikiforov, The energy of graphs and matrices, J. Math. Anal. Appl., 326(2007) 1472-1475. [11] M. R. Oboudi, A new lower bound for the energy of graphs, Linear Algebra Appl., 590(2019) 384-395. [12] M. R. Rajesh Kanna, B. N. Dharmendra, and G. Sridhara, Minimum dominating energy of a graphs, Int. J. Pure Appl. Math., 85(4)(2013) 707-718. [13] S. Sabeti, A. B. Dehkordi, and S. M. Semnani, The minimum edge covering energy of a graph, Kragujevac J. Math. 45(6)(2021) 969-975. [14] D. Stevanovic, Spectral Radius of Graphs, Elsevier, 2015. [15] I. Gutman, The energy of a graph, Ber. Math.-Statist. Sekt. Forschungsz. Graz, 103(1978) 1-22. [16] B. Xu, On signed edge domination numbers of graphs, Discrete Math., 239(1-3)(2001) 179-189. [17] A. Yu, M. Lu, F. Tian, On Spectral radius of graphs, Linear Algebra Appl. 387 (2004) 41-49. | ||
|
آمار تعداد مشاهده مقاله: 16,044 تعداد دریافت فایل اصل مقاله: 7,708 |
||