Geodesic
Spectral bounds for the zero forcing number of a graph
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 3, pp. 971-982 Cet article a éte moissonné depuis la source Library of Science

Voir la notice de l'article

Let Z(G) be the zero forcing number of a simple connected graph G. In this paper, we study the relationship between the zero forcing number of a graph and its (normalized) Laplacian eigenvalues. We provide the upper and lower bounds on Z(G) in terms of its (normalized) Laplacian eigenvalues, respectively. Our bounds extend the existing bounds for regular graphs.
Keywords: zero forcing number, eigenvalue, bound 
@article{DMGT_2024_44_3_a8,
     author = {Chen, Hongzhang and Li, Jianxi and Xu, Shou-Jun},
     title = {Spectral bounds for the zero forcing number of a graph},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {971--982},
     year = {2024},
     volume = {44},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2024_44_3_a8/}
}
TY  - JOUR
AU  - Chen, Hongzhang
AU  - Li, Jianxi
AU  - Xu, Shou-Jun
TI  - Spectral bounds for the zero forcing number of a graph
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2024
SP  - 971
EP  - 982
VL  - 44
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/DMGT_2024_44_3_a8/
LA  - en
ID  - DMGT_2024_44_3_a8
ER  - 
%0 Journal Article
%A Chen, Hongzhang
%A Li, Jianxi
%A Xu, Shou-Jun
%T Spectral bounds for the zero forcing number of a graph
%J Discussiones Mathematicae. Graph Theory
%D 2024
%P 971-982
%V 44
%N 3
%U http://geodesic.mathdoc.fr/item/DMGT_2024_44_3_a8/
%G en
%F DMGT_2024_44_3_a8
Chen, Hongzhang; Li, Jianxi; Xu, Shou-Jun. Spectral bounds for the zero forcing number of a graph. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 3, pp. 971-982. http://geodesic.mathdoc.fr/item/DMGT_2024_44_3_a8/

[1] D. Amos, Y. Caro, R. Davila and R. Pepper, Upper bounds on the k-forcing number of a graph, Discrete Appl. Math. 181 (2015) 1–10. https://doi.org/10.1016/j.dam.2014.08.029

[2] F. Barioli, W. Barrett, S. Butler and et al., AIM Minimum Rank-Special Graphs Work Group, Zero forcing sets and the minimum rank of graphs, Linear Algebra Appl. 428 (2008) 1628–1648. https://doi.org/10.1016/j.laa.2007.10.009

[3] J. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, London, 1976).

[4] A.E. Brouwer and W.H. Haemers, Spectra of Graphs (Springer, New York, 2012). https://doi.org/10.1007/978-1-4614-1939-6

[5] D. Burgarth and V. Giovannetti, Full control by locally induced relaxation, Phys. Rev. Lett. 99(10) (2007) 100501. https://doi.org/10.1103/PhysRevLett.99.100501

[6] S. Butler, Eigenvalues and Structures of Graphs, PhD Thesis (University of California, San Diego, 2008).

[7] Y. Caro and R. Pepper, Dynamic approach to k-forcing, Theory Appl. Graphs 2 (2) (2015) Article 2. https://doi.org/10.20429/tag.2015.020202

[8] F.R.K. Chung, Spectral Graph Theory (CBMS Reg. Conf. Ser. Math., 92 Providence, RI: AMS, 1997). https://doi.org/10.1090/cbms/092

[9] R. Davila and M.A. Henning, Zero forcing versus domination in cubic graphs, J. Comb. Optim. 41 (2021) 553–577. https://doi.org/10.1007/s10878-020-00692-z

[10] M. Gentner and D. Rautenbach, Some bounds on the zero forcing number of a graph, Discrete Appl. Math. 236 (2018) 203–213. https://doi.org/10.1016/j.dam.2017.11.015

[11] T. Kalinowski, N. Kam\u{c}ev and B. Sudakov, The zero forcing number of graphs, SIAM J. Discrete Math. 33 (2019) 95–115. https://doi.org/10.1137/17M1133051

[12] F.A. Taklimi, Zero Forcing Sets for Graphs, PhD Thesis (University of Regina, Regina, Canada, 2013).

[13] W.Q. Zhang, J.F. Wang, W.F. Wang and S. Ji, On the zero forcing number and spectral radius of graphs, Electron. J. Combin. 29 (1) (2022) #P1.33. https://doi.org/10.37236/10638