The helm graph H_n is the graph obtained from an n-wheel graph by adjoining a pendant edge at each node of the cycle. Helm graphs are graceful, with the odd case of n established by Koh et al. 1980 and the even case by Ayel and Favaron. The helm graph H_n is perfect only for n = 3 and even n. Precomputed properties of helm graphs are available in the Wolfram Language using GraphData[{Helm, {n, k}}].

crossed prism graph | cycle graph | flower graph | Möbius ladder | prism graph | web graph | wheel graph