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Article

Keywords:
graph energy; vertex cover number; matching number; bound
Summary:
We give a novel upper bound on graph energy in terms of the vertex cover number, and present a complete characterization of the graphs whose energy equals twice their matching number.
References:
[1] Akbari, S., Ghorbani, E., Zare, S.: Some relations between rank, chromatic number and energy of graphs. Discrete Math. 309 (2009), 601-605. DOI 10.1016/j.disc.2008.09.012 | MR 2499013 | Zbl 1194.05075
[2] Andrade, E., Robbiano, M., Martín, B. San: A lower bound for the energy of symmetric matrices and graphs. Linear Algebra Appl. 513 (2017), 264-275. DOI 10.1016/j.laa.2016.10.022 | MR 3573802 | Zbl 1350.05090
[3] Altındağ, Ş. B. Bozkurt, Bozkurt, D.: Lower bounds for the energy of (bipartite) graphs. MATCH Commun. Math. Comput. Chem. 77 (2017), 9-14. MR 3645362
[4] Caporossi, G., Cvetković, D., Gutman, I., Hansen, P.: Variable neighborhood search for extremal graphs 2. Finding graphs with extremal energy. J. Chem. Inf. Comput. Sci. 39 (1999), 984-996. DOI 10.1021/ci9801419
[5] Cheng, B., Liu, B.: On the nullity of graphs. Electron. J. Linear Algebra 16 (2007), 60-67. DOI 10.13001/1081-3810.1182 | MR 2285832 | Zbl 1142.05336
[6] Coulson, C. A.: On the calculation of the energy in unsaturated hydrocarbon molecules. Proc. Camb. Philos. Soc. 36 (1940), 201-203. DOI 10.1017/S0305004100017175
[7] Cvetković, D., Rowlinson, P., Simić, S.: An Introduction to the Theory of Graph Spectra. London Mathematical Society Student Texts 75. Cambridge University Press, Cambridge (2010). DOI 10.1017/CBO9780511801518 | MR 2571608 | Zbl 1211.05002
[8] Das, K. C., Mojallal, S. A., Gutman, I.: Improving McClelland's lower bound for energy. MATCH Commun. Math. Comput. Chem. 70 (2013), 663-668. MR 3155011 | Zbl 1299.05213
[9] Day, J., So, W.: Graph energy change due to edge deletion. Linear Algebra Appl. 428 (2008), 2070-2078. DOI 10.1016/j.laa.2007.11.009 | MR 2401641 | Zbl 1136.05037
[10] Horn, R. A., Johnson, C. R.: Matrix Analysis. Cambridge University Press, Cambridge (1985). DOI 10.1017/CBO9780511810817 | MR 0832183 | Zbl 0576.15001
[11] Jahanbani, A.: Some new lower bounds for energy of graphs. Appl. Math. Comput. 296 (2017), 233-238. DOI 10.1016/j.amc.2016.10.019 | MR 3572791 | Zbl 1411.05165
[12] Koolen, J. H., Moulton, V.: Maximal energy graphs. Adv. Appl. Math. 26 (2001), 47-52. DOI 10.1006/aama.2000.0705 | MR 1806691 | Zbl 0976.05040
[13] Li, X., Shi, Y., Gutman, I.: Graph Energy. Springer, New York (2012). DOI 10.1007/978-1-4614-4220-2 | MR 2953171 | Zbl 1262.05100
[14] McClelland, B. J.: Properties of the latent roots of a matrix: The estimation of $\pi$-electron energies. J. Chem. Phys. 54 (1971), 640-643. DOI 10.1063/1.1674889
[15] Milovanović, I., Milovanović, E., Gutman, I.: Upper bounds for some graph energies. Appl. Math. Comput. 289 (2016), 435-443. DOI 10.1016/j.amc.2016.05.045 | MR 3515866 | Zbl 1410.05138
[16] Rada, J., Tineo, A.: Upper and lower bounds for the energy of bipartite graphs. J. Math. Anal. Appl. 289 (2004), 446-455. DOI 10.1016/j.jmaa.2003.08.027 | MR 2026917 | Zbl 1034.05034
[17] Wang, L., Ma, X.: Bounds of graph energy in terms of vertex cover number. Linear Algebra Appl. 517 (2017), 207-216. DOI 10.1016/j.laa.2016.12.015 | MR 3592020 | Zbl 1353.05082
[18] Wong, D., Wang, X., Chu, R.: Lower bounds of graph energy in terms of matching number. Linear Algebra Appl. 549 (2018), 276-286. DOI 10.1016/j.laa.2018.03.040 | MR 3784349 | Zbl 1390.05139
[19] Yu, A., Lu, M., Tian, F.: New upper bounds for the energy of graphs. MATCH Commun. Math. Comput. Chem. 53 (2005), 441-448. MR 2134203 | Zbl 1081.05067
[20] Zhou, B.: Energy of a graph. MATCH Commun. Math. Comput. Chem. 51 (2004), 111-118. MR 2063930 | Zbl 1106.05068
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