QM1063 CHAPTER 4
GRAPHS AND DIRECTED GRAPHS
A graph is a finite set V called the vertex set and a collection E of two
element subsets of V. The set E is called the edge set. An element of E is
called an edge. A graph is d
SQQM1063 Discrete Mathematics Matric N0:
QUESTION 1 (4 MARKS)
Determine the truth value of the following propositions:
a) UUM is in Kedah if France is in Africa.
'3: -3 1 E 'T
"“ (2 marks)
F (—7 l 55 F
QUESTION 2 (
CHAPTER 1: LOGIC AND PROOFS
The rules of logic give precise meaning to mathematical statement. These rules are
used to distinguish between valid and invalid mathematical arguments. Because a
major goal of this course is to teach students
SQQM1063 DISCRETE MATHEMATICS
INTRODUCTION TO CODING THEORY
Definition 4.1 An integer is said to be divisible by an integer 0, denoted by |, if there
exists some integer such that = . We write to indicate that is not divisible b
CHAPTER 2: BOOLEAN ALGEBRA
Boolean algebra provides the operations and the rules for working with the set 0,1
. The circuits in computers and other electronic devices have inputs, each of which
either 0 or 1, and produce outputs that are
Definition 1 (Graph Coloring)
A coloring of a simple graph is the assignment of a color of each vertex of the graph so that no two
adjacent vertices are assigned the same color.
Definition 2 (Chromatic Number)
The chromatic number of a grap
The Handshaking Lemma In any graph, the sum of all the
vertex-degree is equal to twice the number of edges.
Since each edge has two ends, it must contribute exactly 2 to the sum of the
degrees. The result follows immediately.
The Following are the c
QM1063 CHAPTER 5
Trees are particularly useful in computer science, where
they are employed in a wide range of algorithms.
A tree is a connected undirected graph with no simple
circuit / without any circles.
A sequence of edges that begins at a vertex of a graph and
travels from vertex to vertex along edges of the graph.
A path that begins and ends at the same vertex.
Simple path / circuit :
A path/circuit is
Introduction to Proof
A theorem is a statement that can be shown to be true. Normally, a theorem consists
of hypothesis and conclusion. If we are given a theorem in the form of p q , then
p is the hypothesis and q is the conclusion. We demonstrate that a
Answer all questions and work in pairs. For each pair, only ONE answer script is required.
Submission due: 12 October 2016 (Wednesday - during class time).
Assume that an expert system restores several premises in its k