Symmetry properties of generalized graph truncations

Abstract

In the generalized truncation construction, one replaces each vertex of a $k$-regular graph $\Gamma$ with a copy of a graph ${\rm Y}$ of order $k$. We investigate the symmetry properties of the graphs constructed in this way, especially in connection to the symmetry properties of the graphs $\Gamma$ and ${\rm Y}$ used in the construction. We demonstrate the usefulness of our results by using them to obtain a classification of cubic vertex-transitive graphs of girths $3$, $4$, and $5$.

20 pages

Cited by in corpus (5)

• Girth-regular graphs
• Symmetries of the Honeycomb toroidal graphs
• Cubic vertex-transitive graphs of girth six
• Cubic factor-invariant graphs of cycle quotient type -- the alternating case
• On the girth and connectivity of cubic graphs with a unique longest cycle