Discussion
There exists a graph with vertex-connectivity \(a\), edge-connectivity \(b\) and the minimum degree \(c\), if :
Answer: C
Such a graph exists for \(a = 2, b = 3, c = 4\).
Whitney's inequality says that for every graph, vertex connectivity \(\le\) edge connectivity \(\le\) minimum degree, i.e. \(a \le b \le c\). Moreover, Chartrand and Harary showed that every triple of positive integers with \(a \le b \le c\) is realised by some graph.
Only option C satisfies \(2 \le 3 \le 4\). Option A has \(a = 4 \gt b = 2\), option B has \(a = 4 \gt b = 3\), and option D has \(b = 4 \gt c = 3\), each violating Whitney's inequality.
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