Fold thickness of some classes of graphs

Thankachan, Reji and Sidharthan, Vaishnavi

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DOI:https://doi.org/10.37193/CMI.2022.02.11

Issue no: Vol 31/2022 no. 2 Tags: fold thickness, uniform folding, singular graphs

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A 1-fold of $G$ is the graph $G'$ 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 sequence of graphs $G = G_0, G_1, G_2, \ldots ,G_k$ , where $G_{i+1}$ is a 1-fold of $G_{i}$ for $i=0,1,2,\ldots ,k-1$ is called a uniform $k$ -folding if all the 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 it was first introduced in [Campeña, F. J. H.; Gervacio, S. V. On the fold thickness of graphs. Arab, J. Math. (Springer) 9 (2020), no. 2, 345–355]. In this paper, we determine fold thickness of $K_n \odot \overline{K_m}$ , $K_n + \overline{K_m}$ , cone graph and tadpole graph.