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Answer
Dec 2, 2014 23:29:36 GMT
Post by maholiza on Dec 2, 2014 23:29:36 GMT
Notice that the value of (n - k)(n - k + 1)/2 decreases when k becomes larger. If a simple graph with n vertices is not connected, it will contain at least 2 connected components. Therefore, the value of k in previous problem is k>2. Then, there are at most (n - 2)(n - 2 + 1)/2 edges in the graph, which contradicts to the condition that the graph has more than (n - 1)(n - 2)/2 edges. Therefore, the graph is connected.
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Answer
Feb 15, 2022 14:39:47 GMT
Post by Vuplic on Feb 15, 2022 14:39:47 GMT
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Answer
Feb 15, 2022 14:42:37 GMT
Post by Vuplic on Feb 15, 2022 14:42:37 GMT
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