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Consider an undirected simple graph G with 300 nodes. The maximum number of edges to be included in G so that the graph is not connected is?

Question

Consider an undirected simple graph G with 300 nodes. The maximum number of edges to be included in G so that the graph is not connected is?

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Solution

To find the maximum number of edges in an undirected simple graph G with 300 nodes, such that the graph is not connected, we need to understand the structure of a disconnected graph.

A disconnected graph can be thought of as a graph where at least one node is not connected to the rest of the graph. The simplest disconnected graph would be a graph where all nodes but one form a complete graph, and the remaining node is isolated.

A complete graph with n nodes has n*(n-1)/2 edges. So, a complete graph with 299 nodes would have 299*(299-1)/2 = 44551 edges.

The remaining node is isolated and does not contribute any edges. So, the maximum number of edges in a disconnected graph with 300 nodes is 44551.

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If every node u in G adjacent to every other node v in G, A graph is said to be Complete Options true false

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