A note on fold thickness of graphs

Authors

• T. Reji Government College Chittur.
• S. Vaishnavi Sree Narayana College Alathur
• Francis Joseph H. Campeña De La Salle University.

Keywords:

fold thickness, uniform folding, singular graphs

Abstract

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 K, G ʘ S , Kmand graph join G +  Km .

Author Biographies

T. Reji, Government College Chittur.

Department of Mathematics.

S. Vaishnavi, Sree Narayana College Alathur

Department of Mathematics.

Francis Joseph H. Campeña, De La Salle University.

Department of Mathematics and Statistics.

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

2023-01-26

How to Cite

[1]
T. Reji, S. Vaishnavi, and F. J. H. . Campeña, “A note on fold thickness of graphs”, Proyecciones (Antofagasta, On line), vol. 42, no. 1, pp. 167-174, Jan. 2023.

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