Tessellate S.T.E.M.S (2019) - Computer Science - College - Set 1 - Objective Problem 4

A graph is said to be k-vertex-conected if it has more than k vertices and remains connected whenever fewer than k vertices are removed. We define $\text{vertex-connectivity} (G)$ to be the smallest $k$ such that the graph is not $k$ -vertex-connected.

A graph is said to be l-edge-conected if it has more than l edges and remains connected whenever fewer than l edges are removed. We define $\text{edge-connectivity} (G)$ to be the smallest $l$ such that the graph is not $l$ -edge-connected.

Let $\delta(G$ be the smallest degree of the vertices of $G$ .

Which of the following is true?

• A) $\text{vertex-connectivity} (G) \leq \text{edge-connectivity} (G) = \delta(G)$
• B) $\text{vertex-connectivity} (G) \leq \text{edge-connectivity} (G) \leq \delta(G)$
• C) $\text{edge-connectivity} (G) \leq \text{vertex-connectivity} (G)\leq \delta(G)$
• D) $\delta(G) \leq \text{vertex-connectivity} (G) \leq \text{edge-connectivity}(G)$

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This problem is a part of Tessellate S.T.E.M.S (2019)