Discussion
Let \(k\), \(k'\) and \(\delta\) be the vertex connectivity, edge connectivity and minimum degree respectively of graph G. Then :
Answer: C
The answer is \(k = k'\) whenever G is 3-regular.
Whitney's inequality says \(k \le k' \le \delta\) for every graph. For a cubic (3-regular) graph the vertex and edge connectivity are always equal: a minimum vertex cut can be turned into an edge cut of the same size because each vertex has only three edges.
The other options contradict Whitney's inequality: \(\delta \le k'\) and \(k' \le k\) reverse it (they hold only in the equality case). And \(\delta = k'\) can fail for regular graphs: two copies of \(K_{5}\) with one edge removed from each, joined by two edges, form a 4-regular graph with edge connectivity 2.
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