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

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Southern Illinois University

MATH 101

MIDTERM EXAM

STUDY GUIDE

*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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