Symmetry Parameters for Mycielskian Graphs

Abstract

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.

arXiv admin note: text overlap with arXiv:2007.15284