Let S be the spanning tree of any graph. Prove that if we add any edge to S to unchanged set of vertices, a cycle will be created.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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a) Let S be the spanning tree of any graph. Prove that if we add any edge to S to unchanged set of vertices, a cycle will be created.

b) A graph G is given. How many different spanning trees (not necessarily non-isomorphic to each other) does this graph have? Justify the answer.

 

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