# Algorithms – How to check if given \$ k \$ vertices efficiently create a \$ k \$ clique in an undirected graph \$ G \$

To let $$G = (V, E)$$ Let be an undirected graph with a set vertex $$V$$ and edge set $$E$$, To let $$V & # 39; = {v_1, v_2, …, v_k }$$ be a subset of $$V$$ where degrees of each $$v_i$$ is greater than or equal to $$k$$, Is there a way to check if $$V & # 39;$$ is a $$k$$-clique more efficient than the brute-force algorithm in $$O (k ^ 2)$$? Thank you in advance.