Math 110 Test questions and answers 2025

Math 110 Test questions and answers 2025
Set

a collection of objects (anything)

Graph

a collection of dots (vertices) and lines (edges) where the dots and lines are given by vertex sets
and edge sets.

Simple Graph

a graph w/o loops or multiple edges

Degree of Vertex

number of edges starting and ending at that vertex

Total Degree of Graph

the sum of the vertex degrees

Therom 1

the total degree of a graph is always an even number

Even/Odd Vertex

a vertex is called even or odd depending on whether its degree is even of odd

Therom 2

in any graph, there is an even number of odd vertices.

Adjacent

two edges are ______ if they share a vertex

Path

a sequence of distinct adjacent edges (cannot repeat an edge)

, Circuit

a path that starts and ends at the same vertex (cannot repeat an edge)

Connected

a graph is ________ if you can go between any two vertices with a path

Bridge

an edge in a graph whose removal disconnects the graph

Isolated Vertex

a vertex not connected to the graph or edge

Euler Path Therom

a connected graph has an Euler path if and only if it has exactly two odd vertices

Euler Path

a path that hits every edge once

Euler Circuit Therom

in a connected graph an Euler circuit is possible if and only if there are exactly zero odd vertices

Eulerization

the process of duplicating edges until no odd vertices remain (# of odd vertices/2)

Semi-Eulerization

the process of duplicating edges until two odd vertices remain

Hamilton Path

in a connected graph, a path that hits every vertex once and only once.

Hamilton Circuit

a hamilton path that starts and ends at the same vertex