Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
7.2 Eulerian Paths
Definition 1. An Eulerian path is one that uses every edge in a graph exactly once. An
Eulerian circuit is an Eulerian path that is a cycle, i.e. it ends at the same vertex that it
starts at.
Not every graph has an Eulerian path or circ
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
6. Relations
When we were talking about logic earlier we considered predicates. These were rules (or
functions) that took one or more objects and returned a value of true or false depending
on whether or not the object(s) had some property or were related
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
5.3 Second Order Recurrence Relations
In the previous section we saw how to solve first order linear recurrence relations. This
is when an is given by a linear formula of an1, i.e.
an = pnan1 + sn
where pn and sn are given sequences. In this section and
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
7. Graphs
A graph is the same as a relation, only with different terminology. Graph terminology
(instead of relation terminology) tends to be used with applications to real world
situations, which will be the emphasis in this chapter.
Let's momentarily ig
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
6.2 Partial Orderings
In the previous section we talked about equivalence relations which were generalizations
of equality. In this section we consider partial orderings which are generalizations of
lessthanor equalto.
Definition 1.
i.
ii.
iii.
A relat
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
4
Permuatations and Combinations
This chapter is concerned with counting the number of ways one can do something. A typical example is
how many ways can one form a committee of three people who are chosen from a pool of six people.
Section 1 contains some
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
7.3 Shortest Paths
In this section we discuss an algorithm to find a shortest path from one vertex to another
in a graph where the edges have weights.
Example 1. A company has offices in the eight cities that are the vertices in the graph
below. There are
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
4.3 Combinations
Application to Binomials. Combinations arise when we expand a power (a + b)n of a
binomial a + b. Here is the case n = 2.
(a + b)2 = (a + b)(a + b) = a(a + b) + b(a + b)
=
= a2 + + b2
= a2 + + b2
= a2 + k1ab + b2
= a2 + 2ab + b2
Here is t
Discrete Mathematical Methods in Computer Engineering
MATH 276

Fall 2014
5. Recurrence Relations
We have already encountered a number of recurrence relations when we talked about
recursion. Now we look at more situations in which they arise and techniques for getting
explicit formulas for the sequence they define.
5.1 Modeling