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Discrete Mathematics Q&A Archive of December 24, 2022

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December 24 of 2022

a graph of order 4 whose vertices have degrees 1,3,3,3
Q)Give an example of the following or explain why no such example exists a graph of order 4 whose vertices have degrees 1,3,3,3 a graph of order 7 whose vertices have degrees 1,2,2,2,3,3,7 a graph of order 7 whose vertices have degrees 1,1,1,2,2,3,3.
Assignment 1. By method of mathematical induction, prove that i. \( \quad a+a r^{2}+\cdots a r^{n-1}=\frac{a\left(1-r^{n}\right)}{1-r}, 0 \leq r<1, \forall n \in N \) ii. \( \quad 1^{2}+2^{2}+\cdots n^{2}=\frac{n(n+1)(2 n-1)}{6}, \forall n \in N \) 2. Define and classify the recurrence relationā€¦
\begin{tabular}{|l|l|l|l|} \hline b) & Write a 'C' program to generate prime numbers up to a given number. & \( \mathrm{CO} 2 \) & \( \mathrm{~L}-3 \) \\ \hline \end{tabular}
x is an odd number. The largest odd number preceding x is :
consequences
Assignment 1. By method of mathematical induction, prove that i. \( \quad a+a r^{2}+\cdots a r^{n-1}=\frac{a\left(1-r^{n}\right)}{1-r}, 0 \leq r<1, \forall n \in N \) ii. \( \quad 1^{2}+2^{2}+\cdots n^{2}=\frac{n(n+1)(2 n-1)}{6}, \forall n \in N \) 2. Define and classify the recurrence relationā€¦
x is an odd number. The largest odd number preceding x is :
consequences