Let $G=(V(G),E(G))$ be a graph and a set of $X \subseteq V(G)$. $X$ is a mutual-visibility set if there exists a shortest path between vertices of $X$ without further vertices from $X$. Mutual-visibility of a graph $G$ is the cardinality of any largest mutually visible set, $\mu(G)=|X|$. Let $X_t \subseteq V(G)$ be a set. $X_t$ is total mutual-visibility set if there exists a shortest path between any two vertices of $V(G)$ without further vertices from $X_t$. The cardinality of any largest total mutual visibility set $X_t$ is called the total mutual-visibility number of the graph $G$, denoted as $\mu_t(G)=|X_t|$. Lower and upper bounds for $\mu(G)$ and $\mu_t(G)$ are given using various graph invariants. Exact values are given for certain graph families and their products. It is proven that the problem is NP-complete.
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