A note on fold thickness of graphs
DOI:
https://doi.org/10.22199/issn.0717-6279-5655Keywords:
fold thickness, uniform folding, singular graphsAbstract
A 1-fold of G is the graph G0 obtained from a graph G by identifying two nonadjacent vertices in G having at least one common neighbor and reducing the resulting multiple edges to simple edges. A uniform k-folding of a graph G is a sequence of graphs
G = G0, G1, G2,...,Gk, where Gi+1 is a 1-fold of Gi for
i = 0, 1, 2,...,k − 1 such that all graphs in the sequence are singular or all of them are nonsingular. The largest k for which there exists a uniform k- folding of G is called fold thickness of G and this concept was first introduced in [1]. In this paper, we determine fold thickness of corona product graph G ʘ Km , G ʘ S , Kmand graph join G + Km .
References
F. J. Campeña and S. V. Gervacio, “On the fold thickness of graphs”, Arabian Journal of Mathematics, vol. 9, no. 2, pp. 345–355, 2020. https://doi.org/10.1007/s40065-020-00276-z
C. R. Cook and A. B. Evans, “Graph folding”, Congressus numerantium, vol 23-24, pp. 305-314, 1979.
S. V. Gervacio, “Singularity of graphs in some special clases”, Transactions of National Academy of Sciences Technology, vol. 13, pp. 367-373, 1991.
S. V Gervacio, “Trees with diameter less than 5 and non-singular complement”, Discrete Mathematics, vol. 151, no. 1-3, pp. 91-97, 1996. https://doi.org/10.1016/0012-365x(94)00086-x
S. V. Gervacio and R. C. Guerrero and H. M. Rara, “Folding wheels and fans”, Graphs and Combinatorics, vol. 18, no. 4, pp. 731-737, 2002. https://doi.org/10.1007/s003730200058
R. Frucht and F. Harary, “On the corona of two graphs”. Aequationes mathematicae, vol. 4, pp. 322-325, 1970. https://doi.org/10.1007/BF01844162
Published
How to Cite
Issue
Section
Copyright (c) 2023 T. Reji, S. Vaishnavi, Francis Joseph H. Campeña
This work is licensed under a Creative Commons Attribution 4.0 International License.
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
