Abstract
A global forcing set for maximal matchings of a graph \(G=(V(G), E(G))\) is a set \(S \subseteq E(G)\) such that \(M_1\cap S \ne M_2 \cap S\) for each pair of maximal matchings \(M_1\) and \(M_2\) of G. The smallest such set is called a minimum global forcing set, its size being the global forcing number for maximal matchings \(\phi _{gm}(G)\) of G. In this paper, we establish lower and upper bounds on the forcing number for maximal matchings of the corona product of graphs. We also introduce an integer linear programming model for computing the forcing number for maximal matchings of graphs.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adams, P., Mahdian, M., Mahmoodian, E.S.: On the forced matching numbers of bipartite graphs. Discrete Math. 281, 1–12 (2004)
Biedl, T., Demaine, E.D., Kobourov, S.G., Duncan, C.A., Fleischer, R.: Tight bounds on maximal and maximum matchings. Discrete Math. 285, 7–15 (2004)
Cigher, S., Vukičević, D., Diudea, M.V.: On Kekulé structures count. J. Math. Chem. 45, 279–286 (2009)
Diwan, A.A.: The minimum forcing number of perfect matchings in the hypercube. Discrete Math. 342, 1060–1062 (2019)
Došlić, T., Zubac, I.: Counting maximal matchings in linear polymers. ARS Math. Contemp. 11, 255–276 (2016)
Feng, X., Zhang, L., Zhang, M.: Kekulé structures of honeycomb lattice on Klein bottle and Möbius strip. J. Math. Anal. Appl. 496, 124790 (2021)
Klavžar, S., Tavakoli, M.: Edge metric dimensions via hierarchical product and integer linear programming. Optim. Lett. 15, 1993–2003 (2021)
Klavžar, S., Tavakoli, M.: Dominated and dominator colorings over (edge) corona and hierarchical products. Appl. Math. Comput. 390, 125647 (2021)
Kristiana, A.I., Utoyo, M.I., Alfarisi, R.: Dafik, \(r\)-dynamic coloring of the corona product of graphs. Discrete Math. Algorithms Appl. 12, 2050019 (2020)
Lovász, L., Plummer, M.D.: Matching Theory. North-Holland, Amsterdam (1986)
Sedlar, J.: The global forcing number of the parallelogram polyhex. Discrete Appl. Math. 160, 2306–2313 (2012)
Sumner, D.P.: Randomly matchable graphs. J. Graph Theory 3, 183–186 (1979)
Tavakoli, M.: Global forcing number for maximal matchings under graph operations. Control Optim. Appl. Math. 4, 53–63 (2019)
Tratnik, N., Žigert Pleteršek, P.: Saturation number of nanotubes. ARS Math. Contemp. 12, 337–350 (2017)
Vukičević, D., Zhao, S., Sedlar, J., Xu, S., Došlić, T.: Global forcing number for maximal matchings. Discrete Math. 341, 801–809 (2018)
Yannakakis, M., Gavril, F.: Edge dominating sets in graphs. SIAM J. Appl. Math. 38, 364–372 (1980)
Yoong, K.-K., Hasni, R., Irfan, M., Taraweh, I., Ahmad, A., Lee, S.-M.: On the edge irregular reflexive labeling of corona product of graphs with path. AKCE Int. J. Graphs Comb. 18, 53–59 (2021)
Zhang, Y., Zhang, H.: Hexagonal systems with the one-to-one correspondence between geometric and algebraic Kekulé structures. Discrete Appl. Math. 238, 144–157 (2018)
Zhao, L., Zhang, H.: On the anti-Kekulé number of \((4,5,6)\)-fullerenes. Discrete Appl. Math. 283, 577–589 (2020)
Zito, M.: Small maximal matchings in random graphs. Theor. Comput. Sci. 297, 487–507 (2003)
Acknowledgements
Sandi Klavžar acknowledges the financial support from the Slovenian Research Agency (research core funding P1-0297 and projects N1-0095, J1-1693, J1-2452).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Klavžar, S., Tavakoli, M. & Abrishami, G. Global forcing number for maximal matchings in corona products. Aequat. Math. 96, 997–1005 (2022). https://doi.org/10.1007/s00010-022-00869-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00010-022-00869-3