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# Polygonal graphs

A *near-polygonal* graph is a graph Γ which has a set
C of m-cycles for some positive integer m such that each 2-claw
of Γ is contained in exactly one cycle in C.
If m is the girth of Γ then the graph is called *polygonal*.
The 1-skeleton of a regular solid is polygonal.

All rectagraphs are 4-gonal graphs;
all (0,2)-graphs are near 4-gonal graphs.

The Petersen graph and the
Perkel graph and the J_{1} graph
are 5-gonal.

## References

M. Perkel,
*Bounding the valency of polygonal graphs with odd girth*,
Can. J. Math. **31** (1979) 1307-1321.
M. Perkel,
*Near-polygonal graphs*,
Ars. Comb. **26A** (1988) 149-170.

M. Perkel and C.E. Praeger,
*Polygonal graphs: New families and an approach to their analysis*,
Congressus Numerantium **124** (1997) 161-173.

M. Perkel, C.E. Praeger & R. Weiss,
*On Narrow Hexagonal Graphs with a 3-Homogeneous Suborbit*,
J. of Algebraic Combinatorics **13** (2001) 257-273.

Cai Heng Li and Ákos Seress,
*Symmetrical path-cycle covers of a graph and polygonal graphs*,
JCT (A) **114** (2007) 35-51.