# Journal of the Ramanujan Mathematical Society

Volume 36, Issue 4, December 2021 pp. 291–299.

Fold thickness of graphs

**Authors**:
T. Reji and S. Vaishnavi

**Author institution:**Government College, Chittur, Palakkad, Kerala 678~104, India

**Summary: **
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 is
called a 1-fold of G. A uniform k-folding of a graph G is a
sequence of graphs G = G{0}, G{1}, G{2}, … , G{k}, where
G{i+1} is a 1-fold of G{i} 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 lollipop graph, web graph, helm graph
and rooted product of complete graphs and paths.

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