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Improved bounds for Kirchhoff index of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 18، دوره 8، شماره 1، خرداد 2023، صفحه 243-251 اصل مقاله (378.6 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2022.27492.1275 | ||
| نویسندگان | ||
| Ş. Burcu Bozkurt Altındağ* 1؛ Marjan Matejić2؛ Igor Milovanović2؛ Emina Milovanović2 | ||
| 1No | ||
| 2Faculty of Electronic Engineering, University of Niš, Niš, Serbia | ||
| چکیده | ||
| Let $G$ be a simple connected graph with n vertices. The Kirchhoff index of $G$ is defined as $Kf (G) = n\sum_{i=1}^{n-1}1/μ_i$, where $\mu_1\ge \mu_2\ge \dots\ge \mu_{n-1}>\mu_n=0$ are the Laplacian eigenvalues of $G$. Some bounds on $Kf (G)$ in terms of graph parameters such as the number of vertices, the number of edges, first Zagreb index, forgotten topological index, etc., are presented. These bounds improve some previously known bounds in the literature. | ||
| کلیدواژهها | ||
| Laplacian eigenvalues (of graph)؛ topological indices؛ Kirchhoff index | ||
| مراجع | ||
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[1] M. Bianchi, A. Cornaro, J.L. Palacios, and A. Torriero, Bounds for the Kirchho index via majorization techniques, J. Math. Chem. 51 (2013), no. 2, 569-587.
[2] P. Biler and A. Witkowski, Problems in Mathematical Analysis, CRC Press, New York, 2017.
[3] K.C. Das, A sharp upper bound for the number of spanning trees of a graph, Graphs Combin. 23 (2007), no. 6, 625-632.
[4] K.C. Das and K. Xu, On relation between Kirchho index, Laplacian-energy-like invariant and Laplacian energy of graphs, Bull. Malays. Math. Sci. Soc. 39 (2016), no. 1, 59-75.
[5] Kinkar C Das, On the Kirchho index of graphs, Z. Naturforschung 68a (2013), no. 8-9, 531-538.
[6] B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015), no. 4, 1184-1190.
[7] R. Grone and R. Merris, The Laplacian spectrum of a graph ii, SIAM J. Discrete Math. 7 (1994), no. 2, 221-229.
[8] I. Gutman and B. Mohar, The quasi-Wiener and the Kirchho indices coincide, J. Chem. Inf. Comput. Sci. 36 (1996), no. 5, 982-985.
[9] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), no. 4, 535-538.
[10] D.J. Klein and M. Randić, Resistance distance, J. Math. Chem. 12 (1993), no. 1, 81-95.
[11] J. Li, W.C. Shiu, and W.H. Chan, The laplacian spectral radius of some graphs, Linear Algebra Appl. 431 (2009), no. 1-2, 99-103.
[12] R. Merris, Laplacian matrices of graphs: A survey, Linear Algebra Appl. 197&198 (1994), 143-176.
[13] I. Milovanović, I. Gutman, and E. Milovanović, On Kirchho and degree Kirchho indices, Filomat 29 (2015), no. 8, 1869-1877.
[14] I. Milovanović and E. Milovanović, Bounds of Kirchho and degree Kirchho indices, Bounds in Chemical Graph Theory { Mainstreams (K.C. Das, E. Milovanović, I. Milovanović, I. Gutman, B. Furtula, Ed.), Univ. Kragujevac, Kragujevac, 2017, pp. 93-119. [15] I. Milovanović and E. Milovanović, On some lower bounds of the Kirchho index, MATCH Commun. Math. Comput. Chem. 78 (2017), 169-180.
[16] I. Milovanović, E. Milovanović, E. Glogić, and M. Matejić, On Kirchho index, Laplacian energy and their relations, MATCH Commun. Math. Comput. Chem. 81 (2019), no. 2, 405-418.
[17] D.S. Mitrinović and P.M. Vasić, Analytic inequalities, Springer, Berlin, 1970.
[18] B. Mohar, The Laplacian spectrum of graphs, Graph Theory, Combinatorics, and Applications (G. Alavi, O.R. Chartrand, and A.J.S. Oellermann, eds.), Wiley, New York, 1991, pp. 871-898.
[19] J.L. Palacios, Some additional bounds for the Kirchho index, MATCH Commun. Math. Comput. Chem. 75 (2016), no. 2, 365-372.
[20] S. Pirzada, H.A. Ganie, and I. Gutman, On Laplacian-energy-like invariant and Kirchho index, MATCH Commun. Math. Comput. Chem. 73 (2015), no. 1, 41-59.
[21] B.C. Rennie, On a class of inequalities, J. Austral. Math. Soc. 3 (1963), no. 4, 442-448.
[22] O. Rojo, R. Soto, and H. Rojo, An always nontrivial upper bound for Laplacian graph eigenvalues, Linear Algebra Appl. 312 (2000), no. 1-3, 155-159.
[23] S. Rosset, Normalized symmetric functions, Newton's inequalities, and a new set of stronger inequalities, Amer. Math. Soc. 96 (1989), no. 9, 815-819.
[24] Y. Yang, H. Zhang, and D.J. Klein, New Nordhaus-Gaddum-type results for the Kirchho index, J. Math. Chem. 49 (2011), no. 8, 1587-1598.
[25] B. Zhou and N. Trinajstić, A note on Kirchho index, Chem. Phys. Lett. 455 (2008), no. 1-3, 120-123.
[26] B. Zhou and N. Trinajstić, On resistance-distance and Kirchho index., J. Math. Chem. 46 (2009), no. 1, 283-289.
[27] H.-Y. Zhu, D.J. Klein, and I. Lukovits, Extensions of the Wiener number, J. Chem. Inf. Comput. Sci. 36 (1996), no. 3, 420-428.
[28] E. Zogic and E. Glogic, A note on the Laplacian resolvent energy, Kirchho index and their relations, Discrete Math. Lett. 2 (2019), no. 1, 32-37.
[29] P. Zumstein, Comparison of spectral methods through the adjacency matrix and the Laplacian of a graph, Th Diploma, ETH Zurich, 2005.
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