
تعداد نشریات | 43 |
تعداد شمارهها | 1,685 |
تعداد مقالات | 13,830 |
تعداد مشاهده مقاله | 32,661,770 |
تعداد دریافت فایل اصل مقاله | 12,915,931 |
Some chemical indices related to the number of triangles | ||
Transactions on Combinatorics | ||
مقاله 4، دوره 12، شماره 1، خرداد 2023، صفحه 27-35 اصل مقاله (406.3 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/toc.2022.128093.1843 | ||
نویسنده | ||
Mihrigul Wali* | ||
School of Mathematical Sciences, Xiamen University, 361005, Fuzhou, Xiamen, P. R. China. | ||
چکیده | ||
Many chemical indices have been invented in theoretical chemistry, such as the Zagreb index, the Lanzhou index, the forgotten index, the Estrada index etc. In this paper, we show that the first Zagreb index is only related to the sum of the number of triangles in a graph and the number of triangles in its complement. Moreover, we determine the sum of the first and second Zagreb index, the Lanzhou index and the forgotten index for a graph and its complement in terms of the number of triangles in a graph and the number of triangles in its complement. Finally, we estimate the Estrada index in terms of order, size, maximum degree and the number of triangles. | ||
کلیدواژهها | ||
Zagreb index؛ Lanzhou index؛ Forgotten index؛ Estrada index؛ Triangles | ||
مراجع | ||
[1] A. W. Goodman, On sets of acquaintances and strangers at any party, Amer. Math. Monthly, 66 (1959) 778–783. [2] B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem., 53 (2015) 1184-1190. [3] B. Zhou and Z. B. Du, Some Lower Bounds for Estrada Index, Iranian Journal of Mathematical Chemistry, 1 (2010) 67–72. [4] D. Vukiˇcevi´c, L. Qiuli, J. Sedlar and T. Doˇsli´c, Lanzhou index, MATCH Commun. Math. Comput. Chem., 80 (2018) 863–876. [5] D. Cvetkovi´c, M. Doob and H. Sachs, Spectra of Graphs-Theory and Application, Academic Press, New York, 1980. [6] E. Estrada, Characterization of 3D molecular structure, Chem. Phys. Lett., 319 (2000) 713–718. [7] E. Estrada, Rodr´ıguez-Val´azquez, Randi´c, M: Atomic branching in molecules, Int. J. Quant. Chem., 106 (2006) 823–832. [8] E. Estrada, Rodr´ıguez-Val´azquez, Subgraph centrality in complex networks, Phys. Rev. E, 71 (2005). [9] E. A. Nordhaus and J. Gaddum, On complementary graphs, Amer. Math. Monthly, 63 (1956) 175–177. [10] G. Lorden, Blue-empty chromatic graphs, Amer. Math. monthly, 69 (1962) 114–119. [11] I. Gutman and J. Toˇsovi´c, Testing the quality of molecular structure descriptors, Vertex-degree-based topological indices, J. Serb. Chem. Soc., 78 (2013) 805–810. [12] I. Gutman, Remark on the moment expansion of total π-electron energy, Theor. Chim. Acta, 83 (1992) 313–318. [13] I. Gutman, S. Markovi´c and A. Vesovi´c, Estrada, Approximating total -electron energy in terms of spectral moments, A quantitative approach, J. Serb. Chem. Soc., 63 (1998) 639–646. [14] K. C. Das, Maximizing the sum of the squares of the degrees of a graph, Discrete Math., 285 (2004) 57–66. [15] K. C. Das, K. Das and I. Gutman, Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem., 52 (2004) 103–112. [16] L. Zhang and W. Baoyindureng, The Nordhaus-Goddum-type inequalities for some chemiacal indices, MATCH Commum. Comput. Chem., 54 (2005) 189–194. [17] S. M. Hosamani and B. Basavanagoud, New Upper Bounds for the First Zagreb Index, MATCH Commun. Math. Comput. Chem., 74 (2015) 97–101. [18] X. D. Chen and J. G. Qian, Bounds on the number of closed walks in a graph and its applications, Journal of Inequalities and Applications, 199 (2014). | ||
آمار تعداد مشاهده مقاله: 221 تعداد دریافت فایل اصل مقاله: 259 |