Remarks on the bounds of graph energy in terms of vertex cover number or matching number

Xiaodan Chen; Xiaoqian Liu

Czechoslovak Mathematical Journal (2021)

  • Volume: 71, Issue: 2, page 309-319
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Chen, Xiaodan, and Liu, Xiaoqian. "Remarks on the bounds of graph energy in terms of vertex cover number or matching number." Czechoslovak Mathematical Journal 71.2 (2021): 309-319. <http://eudml.org/doc/297438>.

@article{Chen2021,
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.},
author = {Chen, Xiaodan, Liu, Xiaoqian},
journal = {Czechoslovak Mathematical Journal},
keywords = {graph energy; vertex cover number; matching number; bound},
language = {eng},
number = {2},
pages = {309-319},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Remarks on the bounds of graph energy in terms of vertex cover number or matching number},
url = {http://eudml.org/doc/297438},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Chen, Xiaodan
AU - Liu, Xiaoqian
TI - Remarks on the bounds of graph energy in terms of vertex cover number or matching number
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 2
SP - 309
EP - 319
AB - 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.
LA - eng
KW - graph energy; vertex cover number; matching number; bound
UR - http://eudml.org/doc/297438
ER -

References

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  1. Akbari, S., Ghorbani, E., Zare, S., 10.1016/j.disc.2008.09.012, Discrete Math. 309 (2009), 601-605. (2009) Zbl1194.05075MR2499013DOI10.1016/j.disc.2008.09.012
  2. Andrade, E., Robbiano, M., Martín, B. San, 10.1016/j.laa.2016.10.022, Linear Algebra Appl. 513 (2017), 264-275. (2017) Zbl1350.05090MR3573802DOI10.1016/j.laa.2016.10.022
  3. Altındağ, Ş. B. Bozkurt, Bozkurt, D., Lower bounds for the energy of (bipartite) graphs, MATCH Commun. Math. Comput. Chem. 77 (2017), 9-14. (2017) MR3645362
  4. Caporossi, G., Cvetković, D., Gutman, I., Hansen, P., 10.1021/ci9801419, J. Chem. Inf. Comput. Sci. 39 (1999), 984-996. (1999) DOI10.1021/ci9801419
  5. Cheng, B., Liu, B., 10.13001/1081-3810.1182, Electron. J. Linear Algebra 16 (2007), 60-67. (2007) Zbl1142.05336MR2285832DOI10.13001/1081-3810.1182
  6. Coulson, C. A., 10.1017/S0305004100017175, Proc. Camb. Philos. Soc. 36 (1940), 201-203. (1940) DOI10.1017/S0305004100017175
  7. Cvetković, D., Rowlinson, P., Simić, S., 10.1017/CBO9780511801518, London Mathematical Society Student Texts 75. Cambridge University Press, Cambridge (2010). (2010) Zbl1211.05002MR2571608DOI10.1017/CBO9780511801518
  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. (2013) Zbl1299.05213MR3155011
  9. Day, J., So, W., 10.1016/j.laa.2007.11.009, Linear Algebra Appl. 428 (2008), 2070-2078. (2008) Zbl1136.05037MR2401641DOI10.1016/j.laa.2007.11.009
  10. Horn, R. A., Johnson, C. R., 10.1017/CBO9780511810817, Cambridge University Press, Cambridge (1985). (1985) Zbl0576.15001MR0832183DOI10.1017/CBO9780511810817
  11. Jahanbani, A., 10.1016/j.amc.2016.10.019, Appl. Math. Comput. 296 (2017), 233-238. (2017) Zbl1411.05165MR3572791DOI10.1016/j.amc.2016.10.019
  12. Koolen, J. H., Moulton, V., 10.1006/aama.2000.0705, Adv. Appl. Math. 26 (2001), 47-52. (2001) Zbl0976.05040MR1806691DOI10.1006/aama.2000.0705
  13. Li, X., Shi, Y., Gutman, I., 10.1007/978-1-4614-4220-2, Springer, New York (2012). (2012) Zbl1262.05100MR2953171DOI10.1007/978-1-4614-4220-2
  14. McClelland, B. J., 10.1063/1.1674889, J. Chem. Phys. 54 (1971), 640-643. (1971) DOI10.1063/1.1674889
  15. Milovanović, I., Milovanović, E., Gutman, I., 10.1016/j.amc.2016.05.045, Appl. Math. Comput. 289 (2016), 435-443. (2016) Zbl1410.05138MR3515866DOI10.1016/j.amc.2016.05.045
  16. Rada, J., Tineo, A., 10.1016/j.jmaa.2003.08.027, J. Math. Anal. Appl. 289 (2004), 446-455. (2004) Zbl1034.05034MR2026917DOI10.1016/j.jmaa.2003.08.027
  17. Wang, L., Ma, X., 10.1016/j.laa.2016.12.015, Linear Algebra Appl. 517 (2017), 207-216. (2017) Zbl1353.05082MR3592020DOI10.1016/j.laa.2016.12.015
  18. Wong, D., Wang, X., Chu, R., 10.1016/j.laa.2018.03.040, Linear Algebra Appl. 549 (2018), 276-286. (2018) Zbl1390.05139MR3784349DOI10.1016/j.laa.2018.03.040
  19. Yu, A., Lu, M., Tian, F., New upper bounds for the energy of graphs, MATCH Commun. Math. Comput. Chem. 53 (2005), 441-448. (2005) Zbl1081.05067MR2134203
  20. Zhou, B., Energy of a graph, MATCH Commun. Math. Comput. Chem. 51 (2004), 111-118. (2004) Zbl1106.05068MR2063930

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