Decomposition dimension of corona product of some classes of graphs
DOI:
https://doi.org/10.22199/issn.0717-6279-5466Keywords:
decomposition dimension, corona product, path, cycleAbstract
For an ordered k-decomposition D = {G1, G2,...,Gk} of a connected graph G = (V,E), the D-representation of an edge e is the k-tuple γ(e/D)=(d(e, G1), d(e, G2), ...,d(e, Gk)), where d(e, Gi) represents the distance from e to Gi. A decomposition D is resolving if every two distinct edges of G have distinct representations. The minimum k for which G has a resolving k-decomposition is its decomposition dimension dec(G). In this paper, the decomposition dimension of corona product of the path Pn and cycle Cn with the complete graphs K1 and K2 are determined.
References
G. Chartrand, D. Erwin, M. Raines and P. Zhang, “The decomposition dimension of graphs”, Graphs and Combinatorics, vol. 17, pp. 599-605, 2001. https://doi.org/10.1007/PL00007252
H. Enomoto and T. Nakamigawa, “On the decomposition dimension of tres”, Discrete Mathematics, vol. 252, pp. 219-225, 2002. https://doi.org/10.1016/S0012-365X(01)00454-X
M. Hagita, A. Kundgen and D. B. West, “Probabilistic methods for decomposition dimension of graphs”, Graphs and Combinatorics, vol. 19, pp. 493-503, 2003. [On line]. Available: https://bit.ly/3RHlTD4
F. Harary, R. A. Melter, “On the metric dimension of a graph”, Ars Combinatoria, vol. 15, pp. 191-195, 1976.
M. A. Johnson, “Structure-activity maps for visualizing the graph variables arising in drug design”, Journal of Biopharmaceutical Statistics, vol. 3, pp. 203-236, 1993. https://doi.org/10.1080/10543409308835060
T. Reji and R. Ruby, “Decomposition dimension of cartesian product of some graphs”, Discrete Mathematics Algorithms and Applications, 2022, https://doi.org/10.1142/S1793830922501154
J. A. Rodríguez-Velázquez, I. G. Yero and D. Kuziak, “The partition dimension of corona product graphs”, arXiv:1010.5144v, 2010.
V. Saenpholphat, P. Zhang, “Connected Resolving Decompositions in Graphs”, Mathematica Bohemica, vol. 128, pp. 121-136, 2003. https://doi.org/10.21136/mb.2003.134033
P. J. Slater, “Dominating and reference sets in graphs”, Journal of Mathematical Physics, vol. 22, pp. 445-455, 1988.
I. G. Yero, D. Kuziak, J. A. Rodríguez-Velázquez, “On the metric dimension of corona product graphs”, Computers and Mathematics with Applications, vol. 61, pp. 2793-2798, 2011. https://doi.org/10.1016/j.camwa.2011.03.046
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