Define regular graph. Find the number of edges of a 4-regular graph with 6 vertices.

Find the order of the following recurrences and state whether they are homogeneous or non-homogeneous;

xn+1 2xn-15xn-1

3xn+1 -7xn 4xn-1 2n

Solve the recurrence relation

xn+l -8xn 15xn-1 where X0 and x1 21.

Find the generating function for the sequence

Determine whether the sequence is a solution of the recurrence relation

an an-1 2an-2+ if an 2.

Is a Hamiltonian graph Eulerian Is a Eulerian graph Hamiltonian Show with the help of a suitable example.

Solve an+l 5an for n a0 by Substitution method.

Solve the recurrence

an -7an-1 10an-2 n 2

by Characteristic root method.

Solve the recurrence by using iterative approach:

an 2n a0 =4.

Find the sequence having the generating function G given by

1/1-2x.

Define isomorphic graph. Give an example of the same.

State Euler's formula for the graph.

For the following graph

<img src='./qimages/14220-4b.jpg'>

draw subgraphs

G-e

G

Is a subgraph of a planar graph, planar Justify your answer.

Solve an 4(an-1 with initial condition a0 a1 =l.

For which value of m and n is Km,n a tree?

Show that C6 is a bipartite graph.