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Prove or disapprove each of the following: (a) Every disconnected graph has an isolated vertex. (b)...

Prove or disapprove each of the following:

(a) Every disconnected graph has an isolated vertex.

(b) A graph is connected if and only if some vertex is connected to all other vertices.

(c) If G is a simple, connected, Eulerian graph, with edges e, f that are incident to a common vertex, then G has an Eulerian circuit in which e and f appear consequently.

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