پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 44 |
| تعداد شمارهها | 1,877 |
| تعداد مقالات | 15,278 |
| تعداد مشاهده مقاله | 43,732,113 |
| تعداد دریافت فایل اصل مقاله | 17,564,546 |
Skew Randi'c matrix and skew Randi'c energy | ||
| Transactions on Combinatorics | ||
| مقاله 1، دوره 5، شماره 1، خرداد 2016، صفحه 1-14 اصل مقاله (668.9 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2016.9513 | ||
| نویسندگان | ||
| Ran Gu1؛ Fei Huang1؛ Xueliang Li* 2 | ||
| 1Center for Combinatorics, Nankai University, Tianjin 300071, P.R. China | ||
| 2Center for Combinatorics, Nankai University, Tianjin 300071, China | ||
| چکیده | ||
| Let $G$ be a simple graph with an orientation $\sigma$, which assigns to each edge a direction so that $G^\sigma$ becomes a directed graph. $G$ is said to be the underlying graph of the directed graph $G^\sigma$. In this paper, we define a weighted skew adjacency matrix with Rand'c weight, the skew Randi'c matrix ${\bf R_S}(G^\sigma)$, of $G^\sigma$ as the real skew symmetric matrix $[(r_s)_{ij}]$ where $(r_s)_{ij} = (d_id_j)^{-\frac{1}{2}}$ and $(r_s)_{ji} = -(d_id_j)^{-\frac{1}{2}}$ if $v_i \rightarrow v_j$ is an arc of $G^\sigma$, otherwise $(r_s)_{ij} = (r_s)_{ji} = 0$. We derive some properties of the skew Randi'c energy of an oriented graph. Most properties are similar to those for the skew energy of oriented graphs. But, surprisingly, the extremal oriented graphs with maximum or minimum skew Randi'c energy are completely different, no longer being some kinds of oriented regular graphs. | ||
| کلیدواژهها | ||
| oriented graph؛ skew Randi'c matrix؛ skew Randi'c energy | ||
| مراجع | ||
|
[1] C. Adiga, R. Balakrishnan and W. So, The skew energy of a digraph, Linear Algebra Appl., 432 (2010) 1825-1835. [2] C. Adiga and Z. Khoshbakht, On some inequalities for the skew Laplacian energy of digraphs, J. Inequal. Pure Appl. Math., 10 (2009) 1-6. [3] C. Adiga and M. Smitha, On the skew Laplacian energy of a digraph, Int. Math. Forum, 4 (2009) 1907-1914. [4] B. Bollobas and P. Erd}os, Graphs of extremal weights, Ars Combin., 50 (1998) 225-233. [5] J. A. Bondy and U. S. R. Murty, Graph Theory, Graduate Texts in Mathematics, 244, Springer, New York, 2008. [6] S . B. Bozkurt and D. Bozkurt, Randic energy and Randic Estrada index of a graph, Eur. J. Pure Appl. Math., 5 (2012) 88-96. [7] S . B. Bozkurt and D. Bozkurt, Sharp upper bounds for energy and Randic energy, MATCH Commun. Math. Comput. Chem., 70 (2013) 669-680. [8] S . B. Bozkurt, A. D. Gungor and I. Gutman, Randic sp ectral radius and Randic energy, MATCH Commun. Math. Comput. Chem., 64 (2010) 321-334. [9] S . B. Bozkurt, A. D. Gungor, I. Gutman and A. S C evik, Randic matrix and Randic energy, MATCH Commun. Math. Comput. Chem., 64 (2010) 239-250. [10] M. Cavers, S. Fallat and S. Kirkland, On the normalized Laplacian energy and general Randic index $R_{-1}$ of graphs, Linear Algebra Appl., 433 (2010) 172-190. [11] L. H. Clark and J. W. Mo on, On the general Randic index for certain families of trees, Ars Combin., 54 (2000) 223-235. [12] D. M. Cvetkovic, M. Doob and H. Sachs, Spectra of Graphs{Theory and Application, Academic Press, New York, 1980. [13] B. Furtula and I. Gutman, Comparing energy and Randic energy, Maced. J. Chem. Chem. Eng., 32 (2013) 117-123. [14] I. Gutman, B. Furtula and S . B. Bozkurt, On Randic energy, Linear Algebra Appl., 442 (2014) 50-57. [15] S. Gong and G. Xu, The characteristic p olynomial and the matchings p olynomial of a weighted oriented graph, Linear Algebra Appl., 436 (2012) 3597-3607. [16] R. Gu, F. Huang and X. Li, General Randic matrix and general Randic energy, Trans. Comb., 3 no. 3 (2014) 21-33. [17] R. Gu, F. Huang and X. Li, Randic incidence energy of graphs, Trans. Comb., 3 no. 4 (2014) 1-9. [18] R. Gu, X. Li and J. Liu, Note on three results on Randic energy and incidence energy, MATCH Commun. Math. Comput. Chem., 73 (2015) 61-71. [19] I. Gutman, B. Furtula and S . B. Bozkurt, On Randic energy, Linear Algebra Appl., 442 (2014) 50-57. [20] R. Horn and C. Johnson, Matrix Analysis, Cambridge University Press, 1987. [21] X. Li and J. Wang, Randic energy and Randic eigenvalues, MATCH Commun. Math. Comput. Chem., 73 (2015) 73-80. [22] X. Li and Y. Yang, Sharp b ounds for the general Randic index, MATCH Commun. Math. Comput. Chem., 51 (2004) 155-166. [23] X. Li and Y. Yang, Best lower and upp er b ounds for the Randic index $R_{-1}$ of chemical trees, MATCH Commun. Math. Comput. Chem., 52 (2004) 147-156. [24] Lj. Pavlovic, M. Sto janvoic and X. Li, More on the b est upp er b ound for the Randic index $R_{-1}$ of trees, MATCH Commun. Math. Comput. Chem., 60 (2008) 567-584. [25] M. Randic, On characterization of molecular branching, J. Amer. Chem. Soc., 97 (1975) 660-6615. [26] B. Shader and W. So, Skew sp ectra of oriented graphs, Electron. J. Combin., 16 (2009) 1-6. | ||
|
آمار تعداد مشاهده مقاله: 3,455 تعداد دریافت فایل اصل مقاله: 3,709 |
||