آمار
| تعداد نشریات | 5 |
| تعداد شماره‌ها | 112 |
| تعداد مقالات | 1,271 |
| تعداد مشاهده مقاله | 1,239,117 |
| تعداد دریافت فایل اصل مقاله | 1,098,462 |
New skew equienergetic oriented graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 2، دوره 4، شماره 1، شهریور 2019، صفحه 15-24 اصل مقاله (413.76 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2018.26286.1093 | ||
| نویسندگان | ||
| Xiangxiang Liu1؛ Ligong Wang* 2؛ Cunxiang Duan3 | ||
| 1Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, People's Republic of China | ||
| 2Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, People's Republic of China. | ||
| 3Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, People's Republic of China | ||
| چکیده | ||
| Let $S(G^{\sigma})$ be the skew-adjacency matrix of the oriented graph $G^{\sigma}$, which is obtained from a simple undirected graph $G$ by assigning an orientation $\sigma$ to each of its edges. The skew energy of an oriented graph $G^{\sigma}$ is defined as the sum of absolute values of all eigenvalues of $S(G^{\sigma})$. Two oriented graphs are said to be skew equienergetic if their skew energies are equal. In this paper, we determine the skew spectra of some new oriented graphs. As applications, we give some new methods to construct new non-cospectral skew equienergetic oriented graphs. | ||
| کلیدواژه‌ها | ||
| Oriented graph؛ Skew energy؛ Skew equienergetic | ||
| مراجع | ||
|
[1] N. Abreu, D.M. Cardoso, I. Gutman, E.A. Martins, and M. Robbiano, Bounds for the signless laplacian energy, Linear Algebra Appl. 435 (2011), no. 10, 2365–2374.
[2] C. Adiga, R. Balakrishnan, and W. So, The skew energy of a digraph, Linear Algebra Appl. 432 (2010), no. 7, 1825–1835.
[3] C. Adiga and B.R. Rakshith, More skew-equienergetic digraphs, Commun. Comb. Optim. 1 (2016), no. 1, 55–71.
[4] X.L. Chen, X.L. Li, and H. Lian, 4-regular oriented graphs with optimum skew energy, Linear Algebra Appl. 439 (2013), no. 10, 2948–2960.
[5] D. Cvetković, M. Doob, and H. Sachs, Spectra of Graphs: Theory and Application, Academic Press, New York, 1980.
[6] S.C. Gong and G.H. Xu, 3-regular digraphs with optimum skew energy, Linear Algebra Appl. 436 (2012), no. 3, 465–471.
[7] S.C. Gong, G.H. Xu, and W.B. Zhong, 4-regular oriented graphs with optimum skew energies, European. J. Combin. 36 (2014), 77–85.
[8] L.F. Guo and L.G. Wang, Optimum skew energy of a tournament, Linear Algebra Appl. 530 (2017), 405–413.
[9] L.F. Guo, L.G. Wang, and P. Xiao, 5-regular oriented graphs with optimum skew energy, Appl. Math. Comput. 301 (2017), 43–59.
[10] I. Gutman, The energy of a graph, Ber. Math. Statist. sekt. Forschungsz. Graz. 103 (1978), 1–22.
[11] I. Gutman and X.L. Li, Energies of Graphs-Theory and Applications, Mathematical Chemistry Monograph, No.17, 2016.
[12] I. Gutman, X.L. Li, and J.B. Zhang, Graph energy, in: M. Dehmer and F. Emmert-Streib (eds.) Analysis of Complex Networks: From Biology to Linguistics, Wiley/VCH, Weinheim, 2009, 145–174.
[13] I. Gutman and O. E. Polansky, Mathematical Concepts in Organic Chemistry, Springer, Berlin, 1986.
[14] I. Gutman and B. Zhou, Laplacian energy of a graph, Linear Algebra Appl. 414 (2006), no. 1, 29–37.
[15] Y.P. Hou and T. Lei, Characteristic polynomials of skew-adjacency matrices of oriented graphs, Electron. J. Combin. 18 (2011), no. 1, P156, 12pp.
[16] G. Indulal, I. Gutman, and A. Vijayakumar, On distance energy of graphs, MATCH Commun. Math. Comput. Chem. 60 (2008), 461–472.
[17] K. Ito, The skew energy of tournaments, Linear Algebra Appl. 518 (2017), 144–158.
[18] X.L. Li and H.S. Lian, A survey on the skew energy of oriented graphs, Available at https://arxiv.org/abs/1304.5707v6, 2015.
[19] X.L. Li, Z.M. Qin, K. Yang, and J.F. Wang, Tricyclic oriented graphs with maximal skew energy, Bull. Malays. Math. Sci. Soc. 40 (2017), no. 1, 321–333.
[20] X.L. Li, Y.T. Shi, and I. Gutman, Graph Energy, Springer, New York, 2012.
[21] H.S. Ramane, K.C. Nandeesh, I. Gutman, and X.L. Li, Skew equienergetic digraphs, Trans. Comb. 5 (2016), no. 1, 15–23.
[22] X.L. Shen, Y.P. Hou, and C.Y. Zhang, Bicyclic digraphs with extremal skew energy, Electron. J. Linear Algebra 23 (2012), no. 1, 340–355.
[23] F.L. Tian and D. Wong, Relation between the skew energy of an oriented graph and its matching number, Discrete Appl. Math. 222 (2017), 179–184.
[24] W.H. Wang, Ordering of oriented unicyclic graphs by skew energies, Appl. Math. Comput. 284 (2016), 136–148.
| ||
|
آمار تعداد مشاهده مقاله: 1,037 تعداد دریافت فایل اصل مقاله: 787 |
||