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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Given below are two statements
Statement I: In an undirected graph, number of odd degree vertices is even.
Statement II: In an undirected graph, sum of degrees of all vertices is even.
In light of the above statements, choose the correct answer from the options given below.
Statement I: In an undirected graph, number of odd degree vertices is even.
Statement II: In an undirected graph, sum of degrees of all vertices is even.
In light of the above statements, choose the correct answer from the options given below.
Solution
By Handshaking Theorem, sum of degrees of all vertices in an undirected graph is equal to twice the number of edges.So,
$\sum deg(v)=2|E|$
This is always even. Hence, Statement II is true.
Also, in any undirected graph, the number of vertices having odd degree is always even.
Hence, Statement I is also true.
Therefore, both statements are true.
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