Define vertex connectivity and cut vertex set of any graph G. Find the vertex connectivity and cut vertex set for the following graph:
Vertex connectivity of a graph $G$, denoted by $\kappa(G)$, is the minimum number of vertices whose removal either disconnects the graph or reduces it to a trivial graph (a single vertex). In other words, it measures the resilience of the graph against vertex removal. A graph with higher vertex connectivity is more robust because more vertices need to be removed to _______ _______ _______ _____ ________ ______ ____ ___.
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Express the following statements in symbolic form.
i) There is a man in the park with blue eyes.
ii) Every blue-eyed man in the park is wearing a red hat.
iii) If a man wears no hat, then he has black eyes
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