@Nisha Bharti @Abhrajyoti00 Neither cut vertices nor cut edges exist in a complete graph with $\geq 3$ vertices.

To find cut vertices or cut edges, you have to delete only “one” vertex or “one” edge at a time. The general definition says:

A cut-edge or cut-vertex of a graph is “an” edge or “a” vertex (respectively) whose deletion increases the number of components.

We write $G \ – \ e$ for deleting an edge $e$ and $G \ – \ v$ for deleting a vertex $v.$

Here, you are deleting a set of edges for a complete graph which is denoted by subgraph $G \ - \ M$ where M is the set of edges. When we delete a set of vertices then it is called “Induced Subgraph” which is denoted by $G \ – \ S$ where $S$ is set of vertices.

In case of undirected complete graph with $\geq 3$ vertices, deletion of any of the single edges would not increase the number of components, so here cut edge(s) does not exist but if you have $K_2$ then you will increase the number of component by deleting one edge which is the only edge, so in $K_2,$ there will be one cut edge.

For $K_3,K_4,..$ etc, you will not get any cut edges. You could also verify from wiki.