in Graph Theory
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Do we always need to take some graphs and check options by hit and trial in graph theory or they can be done using some axioms.?
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We can solve this type of problem by assuming graph which holds true for their constraint given,

For statement  1 and 2 ,  graph contain six vertices and have degree = 2 ( for each node )

simple graph  , graph which have no multiple edges and self loop is known as simple graph but it can   be connected or not.

each node have two degree means , each node is connected with two different nodes , because simple graph doesn't have multiple edges or self loop.

Then graph have to be cyclic like [ A - B - C - D - E - F - A ] ,   all  have degree equals to two.

Hence statement one is true.

Second, euler circuit : start from any node , traverse each edge exactly once and come back to the starting node is know as euler circuit, which is true for this graph, hence statement 2 is correct.

Statement 3 :   you can surely draw a graph, which have no self loop and no multiple edges, and have degree equals to three , and it is disconnected.

Hence s1 and s2 is correct , s3 is not.

4 Comments

I have already specified that all statements are true or false on different - different graph, but we have to mark any option out of given.   

Anyways thanks , for noticing !!
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thanks akash. all are false
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here multiple edge meaning parallel edges between two nodes
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1 vote
1 vote
All are Wrong..

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