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Prove that in a tree with maximum degree , there are at least leaves

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20 persons are sitting around a table. How many ways can we choose 3 persons, no two of whom are neighbours?

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Find the number of all 20-digit integers in which no two consecutive digits are the same.

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Suppose the maximum degree of a tree T is 4. If n1(T) = 20, n2(T) = n3(T) = n4(T), find the number of vertices of T.

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Give an example of a connected planar graph with $v$ vertices, $e$ edges and $k$ components such $e=3v-6k$.

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CSIR UGC NET June 2019 Part A Question 5

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CSIR UGC NET June 2019 Part A Question 4

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CSIR UGC NET June 2019 Part A Question 3

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CSIR UGC NET June 2019 Part A Question 2

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CSIR UGC NET June 2019 Part A Question 1

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