Abstract
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.
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S. Akbari, E. Ghorbani, S. Zare: Some relations between rank, chromatic number and energy of graphs. Discrete Math. 309 (2009), 601–605.
E. Andrade, M. Robbiano, B. San Martín: A lower bound for the energy of symmetric matrices and graphs. Linear Algebra Appl. 513 (2017), 264–275.
Ş. B. Bozkurt Altindağ, D. Bozkurt: Lower bounds for the energy of (bipartite) graphs. MATCH Commun. Math. Comput. Chem. 77 (2017), 9–14.
G. Caporossi, D. Cvetković, I. Gutman, P. Hansen: Variable neighborhood search for extremal graphs 2. Finding graphs with extremal energy. J. Chem. Inf. Comput. Sci. 39 (1999), 984–996.
B. Cheng, B. Liu: On the nullity of graphs. Electron. J. Linear Algebra 16 (2007), 60–67.
C. A. Coulson: On the calculation of the energy in unsaturated hydrocarbon molecules. Proc. Camb. Philos. Soc. 36 (1940), 201–203.
D. Cvetković, P. Rowlinson, S. Simić: An Introduction to the Theory of Graph Spectra. London Mathematical Society Student Texts 75. Cambridge University Press, Cambridge, 2010.
K. C. Das, S. A. Mojallal, I. Gutman: Improving McClelland’s lower bound for energy. MATCH Commun. Math. Comput. Chem. 70 (2013), 663–668.
J. Day, W. So: Graph energy change due to edge deletion. Linear Algebra Appl. 428 (2008), 2070–2078.
R. A. Horn, C. R. Johnson: Matrix Analysis. Cambridge University Press, Cambridge, 1985.
A. Jahanbani: Some new lower bounds for energy of graphs. Appl. Math. Comput. 296 (2017), 233–238.
J. H. Koolen, V. Moulton: Maximal energy graphs. Adv. Appl. Math. 26 (2001), 47–52.
X. Li, Y. Shi, I. Gutman: Graph Energy. Springer, New York, 2012.
B. J. McClelland: Properties of the latent roots of a matrix: The estimation of π-electron energies. J. Chem. Phys. 54 (1971), 640–643.
I. Milovanović, E. Milovanović, I. Gutman: Upper bounds for some graph energies. Appl. Math. Comput. 289 (2016), 435–443.
J. Rada, A. Tineo: Upper and lower bounds for the energy of bipartite graphs. J. Math. Anal. Appl. 289 (2004), 446–455.
L. Wang, X. Ma: Bounds of graph energy in terms of vertex cover number. Linear Algebra Appl. 517 (2017), 207–216.
D. Wong, X. Wang, R. Chu: Lower bounds of graph energy in terms of matching number. Linear Algebra Appl. 549 (2018), 276–286.
A. Yu, M. Lu, F. Tian: New upper bounds for the energy of graphs. MATCH Commun. Math. Comput. Chem. 53 (2005), 441–448.
B. Zhou: Energy of a graph. MATCH Commun. Math. Comput. Chem. 51 (2004), 111–118.
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The authors are very grateful to the anonymous referees for their valuable comments and suggestions on this paper, which have contributed to the final preparation of the paper.
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This work was supported by the National Natural Science Foundation of China (No. 11861011).
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Chen, X., Liu, X. Remarks on the Bounds of Graph Energy in Terms of Vertex Cover Number or Matching Number. Czech Math J 71, 309–319 (2021). https://doi.org/10.21136/CMJ.2021.0190-19
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DOI: https://doi.org/10.21136/CMJ.2021.0190-19