Geodesic
Remarks on the bounds of graph energy in terms of vertex cover number or matching number
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 2, pp. 309-319
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/CMJ.2021.0190-19
Classification : 05C50
Keywords: graph energy; vertex cover number; matching number; bound 
@article{10_21136_CMJ_2021_0190_19,
     author = {Chen, Xiaodan and Liu, Xiaoqian},
     title = {Remarks on the bounds of graph energy in terms of vertex cover number or matching number},
     journal = {Czechoslovak Mathematical Journal},
     pages = {309--319},
     year = {2021},
     volume = {71},
     number = {2},
     doi = {10.21136/CMJ.2021.0190-19},
     mrnumber = {4263171},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0190-19/}
}
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
SP  - 309
EP  - 319
VL  - 71
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0190-19/
DO  - 10.21136/CMJ.2021.0190-19
LA  - en
ID  - 10_21136_CMJ_2021_0190_19
ER  - 
%0 Journal Article
%A Chen, Xiaodan
%A Liu, Xiaoqian
%T Remarks on the bounds of graph energy in terms of vertex cover number or matching number
%J Czechoslovak Mathematical Journal
%D 2021
%P 309-319
%V 71
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0190-19/
%R 10.21136/CMJ.2021.0190-19
%G en
%F 10_21136_CMJ_2021_0190_19
Chen, Xiaodan; Liu, Xiaoqian. Remarks on the bounds of graph energy in terms of vertex cover number or matching number. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 2, pp. 309-319. doi: 10.21136/CMJ.2021.0190-19

[1] Akbari, S., Ghorbani, E., Zare, S.: Some relations between rank, chromatic number and energy of graphs. Discrete Math. 309 (2009), 601-605. | DOI | MR | JFM

[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 | MR | JFM

[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

[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

[5] Cheng, B., Liu, B.: On the nullity of graphs. Electron. J. Linear Algebra 16 (2007), 60-67. | DOI | MR | JFM

[6] Coulson, C. A.: On the calculation of the energy in unsaturated hydrocarbon molecules. Proc. Camb. Philos. Soc. 36 (1940), 201-203. | DOI

[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 | MR | JFM

[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 | JFM

[9] Day, J., So, W.: Graph energy change due to edge deletion. Linear Algebra Appl. 428 (2008), 2070-2078. | DOI | MR | JFM

[10] Horn, R. A., Johnson, C. R.: Matrix Analysis. Cambridge University Press, Cambridge (1985). | DOI | MR | JFM

[11] Jahanbani, A.: Some new lower bounds for energy of graphs. Appl. Math. Comput. 296 (2017), 233-238. | DOI | MR | JFM

[12] Koolen, J. H., Moulton, V.: Maximal energy graphs. Adv. Appl. Math. 26 (2001), 47-52. | DOI | MR | JFM

[13] Li, X., Shi, Y., Gutman, I.: Graph Energy. Springer, New York (2012). | DOI | MR | JFM

[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

[15] Milovanović, I., Milovanović, E., Gutman, I.: Upper bounds for some graph energies. Appl. Math. Comput. 289 (2016), 435-443. | DOI | MR | JFM

[16] Rada, J., Tineo, A.: Upper and lower bounds for the energy of bipartite graphs. J. Math. Anal. Appl. 289 (2004), 446-455. | DOI | MR | JFM

[17] Wang, L., Ma, X.: Bounds of graph energy in terms of vertex cover number. Linear Algebra Appl. 517 (2017), 207-216. | DOI | MR | JFM

[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 | MR | JFM

[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 | JFM

[20] Zhou, B.: Energy of a graph. MATCH Commun. Math. Comput. Chem. 51 (2004), 111-118. | MR | JFM

Cité par Sources :