Symmetry Parameters for Mycielskian Graphs

9 Mar 2021  ·  Debra Boutin, Sally Cockburn, Lauren Keough, Sarah Loeb, K. E. Perry, Puck Rombach ·

The Mycielskian construction, denoted $\mu(G)$, takes a finite simple graph $G$ to a larger graph with of the same clique number but larger chromatic number. The generalized Mycielskian construction, denoted $\mu_t(G)$, takes $G$ to a larger graph with the same chromatic number but with larger odd girth... In this chapter we look at symmetry parameters of $\mu(G)$ and $\mu_t(G)$ in terms of the same parameters of $G$. These symmetry parameters include determining number, distinguishing number, and cost of distinguishing. read more

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