پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 43 |
| تعداد شمارهها | 1,682 |
| تعداد مقالات | 13,762 |
| تعداد مشاهده مقاله | 32,223,307 |
| تعداد دریافت فایل اصل مقاله | 12,752,441 |
Iota energy orderings of bicyclic signed digraphs | ||
| Transactions on Combinatorics | ||
| دوره 10، شماره 3، آذر 2021، صفحه 187-200 اصل مقاله (266.94 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2021.126881.1805 | ||
| نویسندگان | ||
| Xiuwen Yang؛ Ligong Wang* | ||
| School of Mathematics and Statistics, Northwestern Polytechnical University, 710129, Xi’an, Shaanxi, P. R. China | ||
| چکیده | ||
| The concept of energy of a signed digraph is extended to iota energy of a signed digraph. The energy of a signed digraph $S$ is defined by $E(S)=\sum_{k=1}^n|{Re}(z_k)|$, where ${Re}(z_k)$ is the real part of eigenvalue $z_k$ and $z_k$ is the eigenvalue of the adjacency matrix of $S$ with $n$ vertices, $k=1, 2,\ldots,n$. Then the iota energy of $S$ is defined by $E(S)=\sum_{k=1}^n|{Im}(z_k)|$, where ${Im}(z_k)$ is the imaginary part of eigenvalue $z_k$. In this paper, we consider a special graph class for bicyclic signed digraphs $\mathcal{S}_n$ with $n$ vertices which have two vertex-disjoint signed directed even cycles. We give two iota energy orderings of bicyclic signed digraphs, one is including two positive or two negative directed even cycles, the other is including one positive and one negative directed even cycles. | ||
| کلیدواژهها | ||
| Orderings؛ iota energy؛ bicyclic signed digraphs | ||
| مراجع | ||
|
[1] C. Adiga, R. Balakrishnan and W. So, The skew energy of a digraph, Linear Algebra Appl., 432 (2010) 1825–1835.
[2] M .A. Bhat, Energy of weighted digraphs, Discrete Appl. Math., 223 (2017) 1–14.
[3] M. A. Bhat, U. Sameeb and S. Pirzada, Bicyclic signed graphs with minimal and second minimal energy, Linear Algebra Appl., 551 (2018) 18–35. [4] M. A. Bhat and S. Pirzada, Unicyclic signed graphs with minimal energy, Discrete Appl. Math., 226 (2017) 32–39.
[5] K. C. Das, E. Fritscher, L. K. Pinheiro and V. Trevisan, Maximum Laplacian energy of unicyclic graphs, Discrete Appl. Math., 218 (2017) 71–81. [6] K. C. Das and I. Gutman, Bounds for the energy of graphs, Hacet. J. Math. Stat., 45 (2016) 695–703.
[7] B. Deng, X. L. Li, B. Shader and W. So, On the maximum skew spectral radius and minimum skew energy of tournaments, Linear Multilinear Algebra, 66 (2018) 1434–1441. [8] R. C. Dı́az and O. Rojo, Sharp upper bounds on the distance energies of a graph, Linear Algebra Appl., 545 (2018) 55–75. [9] R. Farooq, S. Chand and M. Khan, Iota energy of bicyclic signed digraphs, Asian-Eur. J. Math., 12 (2019) 14 pp.
[10] R. Farooq, M. Khan and F. Ahmad, Extremal iota energy of bicyclic digraphs, Appl. Math. Comput., 303 (2017) 24–33. [11] R. Farooq, M. Khan and S. Chand, On iota energy of signed digraphs, Linear Multilinear Algebra, 67 (2019) 705–724.
[12] I. Gutman, The energy of a graph, Ber. Math. Stat. Sekt. Forschungszentrum Graz, 103 (1978) 1–22.
[13] I. Gutman, The energy of a graph: old and new results, in: A. Betten, A. Kohnert, R. Laue, A. Wassermann (Eds.), Algebraic Combinatorics and Applications, Springer, Berlin, (2001) 196–211. [14] I. Gutman and X. L. Li (Eds.), Energies of Graphs – theory and applications, in: Mathematical Chemistry Mono- graphs, University of Kragujevac, Kragujevac, 2016. [15] I. Gutman and S. Wagner, The matching energy of a graph, Discrete Appl. Math., 160 (2012) 2177–2187.
[16] L. F. Guo, L. G. Wang and P. Xiao, 5-regular oriented graphs with optimum skew energy, Appl. Math. Comput., 301 (2017) 43–59. [17] S. Hafeez, R. Farooq and M. Khan, Bicyclic signed digraphs with maximal energy, Appl. Math. Comput., 347 (2019) 702–711. [18] S. Hafeez and M. Khan, Iota energy of weighted digraphs, Trans. Comb., 7 (2018) 55–73.
[19] A. Ilić, Distance spectra and distance energy of integral circulant graphs, Linear Algebra Appl., 433 (2010) 1005– 1014. [20] M. Khan and R. Farooq, On the extremal energy of bicyclic digraphs, J. Math. Inequal., 9 (2015) 799–810.
[21] M. Khan and R. Farooq, On the energy of bicyclic signed digraphs, J. Math. Inequal., 11 (2017) 845–862.
[22] M. Khan, R. Farooq and J. Rada, Complex adjacency matrix and energy of digraphs, Linear Multilinear Algebra, 65 (2017) 2170–2186. [23] X. L. Li, Y. T. Shi and I. Gutman, Graph Energy, Springer, New York, 2012.
[24] X. X. Liu, L. G. Wang and P. Xiao, Ordering of bicyclic graphs by matching energy, MATCH Commun. Math. Comput. Chem., 79 (2018) 341–365. [25] J. Monsalve, J. Rada, Bicyclic digraphs with maximal energy, Appl. Math. Comput., 280 (2016) 124–131.
[26] I. Peña and J. Rada, Energy of digraphs, Linear Multilinear Algebra, 56 (2008) 565–578.
[27] L. K. Pinheiro and V. Trevisan, Maximality of the signless Laplacian energy, Discrete Math., 341 (2018) 33–41.
[28] S. Pirzada and M. A. Bhat, Energy of signed digraphs, Discrete Appl. Math., 169 (2014) 195–205.
[29] L. Wang and X. W Fang, Upper bound of skew energy of an oriented graph in terms of its skew rank, Linear Algebra Appl., 569 (2019) 195–205. [30] D. J. Wang and Y. P. Hou, Bicyclic signed graphs with at most one odd cycle and maximal energy, Discrete Appl. Math., 260 (2019) 244–255. [31] W. G. Xi and L. G. Wang, Bounds for the signless Laplacian energy of digraphs, Indian J. Pure Appl. Math., 48 (2017) 411–421. [32] X. W. Yang and L. G. Wang, On the ordering of bicyclic digraphs with respect to energy and iota energy, Appl. Math. Comput., 339 (2018) 768–778. [33] X. W. Yang and L. G. Wang, Ordering of bicyclic signed digraphs by energy, Filomat, 34 (2020) 4297–4309. | ||
|
آمار تعداد مشاهده مقاله: 179 تعداد دریافت فایل اصل مقاله: 170 |
||