Sample questions
1.
How many integral solutions of
x +x +x +x = 30
1
Satisfy
2.
3.
,
5.
3
, and
4
.
How many ways are there to colour the vertices of the 5-cycle so that adjacent vertices receive
different colours?
Let
4.
,
2
, where a =3a
n
-2a
n-1
+2, and a =a =1. Write A(X) as the quotient of
n-2
0
1
two polynomials.
Show that every automorphism of a tree must fix a vertex or an edge.
Show that there are at most 5 connected simple planar graphs in which every face has the same
degree
and every vertex has the same degree
.
6.
For a given graph G show that the chromatic number
degree
7.
8.
9.
is less than or equal to the maximum
.
Construct a cyclic Steiner Triple system of order 13.
Construct 2 idempotent mutually orthogonal Latin squares of order 4.
Show that a transversal design on nk points with k groups is equivalent to k-2 mutually orthogonal
Latin squares of order n.