Is the complement of the Peterson graph planar? Justify your answer.
The complement of the Petersen graph is not planar. In Discrete Mathematics, a graph is said to be planar if it can be drawn on a plane without any of its edges crossing. The Petersen graph ____ ____ ___ __________ ___ __________ ____ ______ ______ ____.
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Define vertex connectivity and cut vertex set of any graph G. Find the vertex connectivity and cut vertex set for the following graph:
Find the Boolean expression in the DNF form for the function defined in tabular form below:
| x | y | z | |
| 1 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 |
Check whether the following statements are true or not. Justify your answers with a short proof or a counter example
i) If the contrapositive of a statement is true, then the statement itself is also true.
ii) is a linear homogeneous recurrence relation.
iii) A particular solution of the recurrence relationhas the form
iv) There exists a boolean expression in variables
v) If a dice is rolled thrice, then the probability of getting a 6 each time is
vi) Every odd cycle has the same chromatic and edge chromatic numbers.
vii) Every Eulerian graph is Hamiltonian.
viii) 3 4 S gives the number of ways in which any 3 objects can be placed in any 4 boxes.
ix) There exists a self-complementary planar graph on 5 or more vertices.
x) The number of partitions of 6 is 10.
For any statements p,q and r, prove that
How many numbers from 0 to 759 are not divisible by either 3 or 7?
Draw three nonisomorphic induced subgraphs of the following graph, each having the same number of vertices. Justify your choice.
Is there a 4-regular graph on 7 vertices? Justify your answer.