3 problems

Let $G$ be a bicoloured graph with no isolated vertices and no twins, where twins are vertices having identical relevant neighbourhoods. Let $[G]$ denote the parity class of $G$, a…

Let $G$ be the Paley graph of prime order $p$, namely $G=\operatorname{Cay}(\mathbb{Z}_p,S)$ where $S$ is the set of quadratic residues modulo $p$. Let $a,b\in\mathbb{Z}_p^*$ have…

Let $G$ be a co-bipartite unit disk graph, meaning that its vertex set can be partitioned into two cliques, and let the bipartite complement of $G$ be the graph obtained by complem…