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Consider the given statements

S1: In a simple graph G with 6 vertices, if degree of each vertex is 2, then Euler circuit exists in G.

S2:In a simple graph G, if degree of each vertex is 3 then the graph G is connected.

Which of the following is/are true?

2 Answers

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In case of S1

G can have two triangles. As G is disconnected so it can never have Euler's circuit. So S1 is not necessarily true

[unless there are isolated vertices as components]

For S2

it is 3-regular graph but not connected. so S2 is false


PS-pardon me for the poor quality image

 

edited by
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S1: Is False

Since we can make C3 C3 Means 2 cycle graph from 6 vertices. Which will be disconnected and euler cercuit will not exit.

S2 : True.

Since from 6 vertices and each having degree 3.

So only graph which is posible is complete bipartite graph (k3,3).

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