[MATH 101] - Midterm Exam Guide - Comprehensive Notes for the exam (17 pages long!)

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7 Feb 2017
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Southern Illinois University
MATH 101
MIDTERM EXAM
STUDY GUIDE
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*Use whatever case set is used in the problem for the answers online*
D B A
B
C
A C D
DC, BC, AB AB, BC, CD
What do you notice?
*They have the same edges.
*Therefore, the graphs are equivalent
A B D
C E
a) Give Vertex Set, V. A, B, C, D, E
b) Give the edge Set, E. AB, AC, BC, CE, BE, BD, DD, DE, ED
Draw a graph to represent Konigsberg
R
ISL1 ISL2
L
Graph the New England States
VT NH ME
MA
CT RI
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The Degree of a vertex is the number of edges at that vertex.
The Vertex with an even number of edges attached to it is an even vertex
A Vertex with an even number of edges attached to it is an odd vertex.
Two Vertices in a graph are said to be adjacent if there is at least one edge connecting them.
A C D
B E
a. List the vertices adjacent to the vertex a.
C, B
b. List the edges adjacent to ED
CE, CD, BE
c. List the vertices adjacent to vertex C
A, B, D, E
d. What is the degree of Vertex C ie. Find Deg(C)
4
e. What is the degree of Vertex B?
3
f. Is C an even or odd Vertex?
Even (has a degree of 4)
g. Is B an even or odd Vertex?
Odd (has a degree of 3)
h. What is the sum of the degrees of all the vertices?
b- deg 3
a- Deg 3
d- deg 2 2+2+4+3+3=14
c- deg 4
e-deg 3
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