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The normalized signless Laplacian Estrada index of graphs | ||
| Transactions on Combinatorics | ||
| دوره 12، شماره 3، آذر 2023، صفحه 131-142 اصل مقاله (499.36 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2022.127155.1814 | ||
| نویسندگان | ||
| Ş. Burcu Bozkurt Altındağ* 1؛ Emina I. Milovanovic2؛ Marjan Matejic2؛ Igor Milovanovic2 | ||
| 1Yenikent Kardelen Konutları, Selçuklu, Konya, Turkey | ||
| 2Faculty of Electronic Engineering, University of Niš, Niš, Serbia | ||
| چکیده | ||
| Let $G$ be a simple connected graph of order $n$ with $m$ edges. Denote by $% \gamma _{1}^{+}\geq \gamma _{2}^{+}\geq \cdots \geq \gamma _{n}^{+}\geq 0$ the normalized signless Laplacian eigenvalues of $G$. In this work, we define the normalized signless Laplacian Estrada index of $G$ as $NSEE\left(G\right) =\sum_{i=1}^{n}e^{\gamma _{i}^{+}}.$ Some lower bounds on $%NSEE\left( G\right) $ are also established. | ||
| کلیدواژه‌ها | ||
| Normalized signless Laplacian eigenvalues؛ Topological indices (of graph)؛ Estrada index (of graph) | ||
| مراجع | ||
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[1] Ş. B. Bozkurt Altındağ, Note on the sum of powers of normalized signless Laplacian eigenvalues of graphs, Math. Interdisc. Res., 4 (2019) 171–182. [2] Ş. B. Bozkurt Altındağ, Sum of powers of normalized signless Laplacian eigenvalues and Randić (normalized) incidence energy of graphs, Bull. Inter. Math. Virtual Inst., 11 (2021) 135–146. [3] Ş. B. Bozkurt Altındağ, A note on the normalized Laplacian Estrada index of bipartite graphs, MATCH Commun. Math. Comput. Chem., 84 (2020) 369–376. [4] Ş. B. Bozkurt, A. D. Gungor, I. Gutman and A. S. Cevik, Randić matrix and Randić energy, MATCH Commun. Math. Comput. Chem., 64 (2010) 239–250. [5] Ş. B. Bozkurt and D. Bozkurt, Randić energy and Randić Estrada index of a graph, Eur. J. Pure Appl. Math., 5 (2012) 88–96. [6] J. R. Carmona and J. Rodrı́guez, An increasing sequence of lower bounds for the Estrada index of graphs and matrices, Linear Algebra Appl., 580 (2019) 200–211. [7] M. Cavers, S. Fallat and S. Kirkland, On the normalized Laplacian energy and general Randić index R−1 of graphs, Lin. Algebra Appl., 433 (2010) 172–190. [8] X. Chen and Y. Hou, Some results on Laplacian Estrada index of graphs, MATCH Commun. Math. Comput. Chem., 73 (2015) 149–162. [9] B. Cheng and B. Liu, The normalized incidence energy of a graph, Lin. Algebra Appl., 438 (2013) 4510–4519. [10] F. R. K. Chung, Spectral Graph Theory, CBMS Regional Conference Series in Mathematics, 92, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1997. [11] V. Cirtoaje, The best lower bound depended on two fixed variables for Jensen’s inequality with ordered variables, J. Inequal. Appl., (2010) 1–12. [12] G. P. Clemente and A. Cornaro, Novel bounds for the normalized Laplacian Estrada index and normalized Laplacian energy, MATCH Commun. Math. Comput. Chem., 77 (2017) 673–690. [13] D. Cvetković, M. Doob and H. Sachs, Spectra of graphs, Theory and application, Pure and Applied Mathematics, 87, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980 368 pp. [14] D. Cvetković, P. Rowlinson and S. Simić, Signless Laplacian of finite graphs, Linear Algebra Appl., 423 (2007) 155–171. [15] K. C. Das and S. G. Lee, On the Estrada index conjecture, Linear Algebra Appl., 431 (2009) 1351–1359.
[16] K. C. Das, S. A. Mojallal and I. Gutman, Improving McClellands lower bound for energy, MATCH Commun. Math. Comput. Chem., 70 (2013) 663–668. [17] K. C. Das, A. D. Gungor and Ş. B. Bozkurt, On the normalized Laplacian eigenvalues of graphs, Ars Combin., 118 (2015) 143–154. [18] J. A. De la Peňa, I. Gutman and J. Rada, Estimating the Estrada index, Linear Algebra Appl., 427 (2007) 70–76.
[19] E. Estrada, Characterization of 3D molecular structure, Chem. Phys. Lett., 319 (2000) 713–718.
[20] E. Estrada, Characterization of the folding degree of proteins, Bioinformatics, 18 (2002) 697–704.
[21] E. Estrada, Characterization of the amino acid contribution to the folding degree of proteins, Proteins, 54 (2004) 727–737. [22] S. Gao and H. Liu, Sharp bounds on the signless Laplacian estrada index of graphs, Filomat, 28 (2014) 1983–1988.
[23] R. Gu, F. Huang and X. Li, Randić incidence energy of graphs, Trans. Comb., 3 no. 4 (2014) 1–9.
[24] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1988. [25] M. Hakimi–Nezhaad, H. Hua, A. R. Ashrafi and S. Qian, The normalized Laplacian Estrada index of graphs, J. Appl. Math. Inf., 32 (2014) 227–245. [26] J. Li, J. M. Guo and W. C. Shiu, The normalized Laplacian Estrada index of a graph, Filomat, 28 (2014) 365–371.
[27] B. Liu, Y. Huang and J. Feng, A note on the Randić spectral radius, MATCH Commun. Math. Comput. Chem., 68 (2012) 913–916. [28] J. Liu and B. Liu, Bounds of the Estrada index of graphs, Appl. Math. J. Chinese Univ. Ser. B, 25 (2010) 325–330.
[29] A. D. Maden, New bounds on the incidence energy, Randić energy and Randić Estrada index, MATCH Commun. Math. Comput. Chem., 74 (2015) 367–387. [30] R. Merris, Laplacian matrices of graphs, A survey, Lin. Algebra Appl., 197–198 (1994) 143–146.
[31] D. S. Mitrinović, Analytic inequalities, In cooperation with P. M. Vasić, Die Grundlehren der mathematischen Wissenschaften, Band 165, Springer-Verlag, New York-Berlin, 1970. [32] M Randić, On characterization of molecule branching, J. Am. Chem. Soc., 97 (1975) 6609–6615.
[33] Y. Shang, More on the normalized Laplacian Estrada index, Appl. Anal. Discrete Math., 8 (2014) 346–357.
[34] B. Zhou and I. Gutman, More on the Laplacian Estrada index, Appl. Anal. Discrete Math., 3 (2009) 371–378.
[35] P. Zumstein, Comparison of spectral methods through the adjacency matrix and the Laplacian of a graph, Th. Diploma, ETH Zürich (2005). | ||
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