4 problems

Let $R$ be a finite non-commutative CC-ring, meaning that all centralizers of non-central elements of $R$ are commutative, and let $\Gamma_R$ be its commuting graph. Let MSN-integr…

Let $R$ be a finite CC-ring, meaning that the centralizer of every non-central element of $R$ is commutative, and let $\Gamma_R$ be its commuting graph. A graph is CN-hyperenergeti…

Let $\mathbb{F}$ be a field and let $\operatorname{Mat}_n(\mathbb{F})$ be the algebra of $n\times n$ matrices over $\mathbb{F}$. Let $\Gamma(\mathbb{F},n)$ be the graph whose verti…

Let $G$ be a finite group with trivial centre, and let its commuting graph be the graph whose vertices are the non-central elements of $G$, with two distinct vertices adjacent exac…