Contemporary Math 1300
What is a completed graph
A graph in which every pair of vertices is joined by an edge.
What is a connected graph
A graph is connected if it is possible to travel from any vertex to any other vertex of the graph by moving along successive edges.
What is an Eulerian graph?
A graph that contains an Euler circuit has all even vertices
What is a Eulerian path?
A path containing all the edges of a graph; TRACE EVERY EDGE
Hamilton path
A path that passes through all the vertices of a graph exactly once. DON'T HAVE TO TRACE EVERY EDGE.
What is an Eulerian circuit?
An Euler path that begins and ends at the same vertex
Can a graph be traced?
Euler's theorem states that a graph can be traced if it is connected and has zero or two odd vertices.
Eulerian graph
Remove one edge from the graph to the right to make the graph Eulerian. Remove edge AC
What is Euler's theorem?
States that a graph can be traced if it is connected and has zero or two odd vertices.
Use the table to the right to calculate the federal income tax due for a taxable income of $ 16,000.
Tax due is 15%(16,000-7,550) + 755 = 2022.50
∨ or
disjunction = false only when both p and q are false.
∧ and
conjunction = true only when both p and q are true.
Kristin Wilson lives in Rock Hill, South Carolina and wishes to visit relatives in the following South Carolina cities: Sumter, Florence, Columbia and Greenville. In how many ways can she visit each of these cities and return to her home in Rock Hill?
5 total cities. 4x3x2x1= 24 ways
How many Hamilton circuits are in K 8
7x6x5x4x3x2x1=5040
Hamilton circuit
A Hamilton path begins and ends at the same vertex
Eulerian graph
If the given graph is Eulerian, find an Euler circuit in it. If the graph is not Eulerian, first Eulerize it and then find an Euler circuit. Write your answer as a sequence of vertices. Determine an Euler circuit that begins with vertex A in this graph.
Eulerian graph
If the given graph is Eulerian, find an Euler circuit in it. If the graph is not Eulerian, first Eulerize it and then find an Euler circuit. Write your answer as a sequence of vertices. Determine an Euler circuit that begins with vertex B in this graph. The graph is Eulerian. The Euler circuit is BEFDECFADB
Nearest-neighbor algorithm
In a Hamiltonian circuit, start with the assigned vertex. Choose the path with the least weight. Continue this until every vertex has been visited and no vertex's can be visited twice. EABDCFE
If the given graph is Eulerian, find an Euler circuit in it. If the graph is not Eulerian, first Eulerize it and then find an Euler circuit. Write your answer as a sequence of vertices. Determine an Euler circuit that begins with vertex B in this graph.
The graph is Eulerian. The Euler circuit is BEFDECFADB
Rate of inflation
The inflation rate is the percent of increase in prices from the base year to the later year. Multiply the base year price by the decimal inflation rate to find the amount that the price has increased.
Is the given sentence a statement? Amanda called for help.
Yes A statement is a sentence that is either true or false, but not both simultaneously. Some sentences, such as commands, questions, and opinions, are not statements because they cannot be labeled as true or false
~ Not
negation
De Morgan's Law
~(pvq) equals ~p∧~q
