GE MATH- FINALS

Next digit; d2

- indicates the country in which the publisher is incorporated (either 0 or 1; what digit of ISBN?

Zeller's congruence

-a formula that gives the day of the week for any date on the Gregorian calendar

Hamiltonian

A graph is Hamiltonian if and only if it has a Hamiltonian circuit. In graph, each vertex of a Hamiltonian circuit is incident to 2 edges.

2-colorable graph theorem

A graph is ___-colorable if and only if it has no circuits that consist of an odd number of vertices

Planar Graph

A graph that can be drawn without any edges crossing

Planarity

A term used to describe a composition where figures and objects are arranged parallel to the picture plane

Leonard Euler (1707 - 1783)

American Mathematician and logician introduced this formal definition of Relation

Dirac's theorem

Consider a connected graph with at least three vertices and no multiple edges. Let n be the number of vertices in the graph. If every vertex has a degree of at least n/2 , then the graph must be Hamiltonian.

ISBN or International Standard Book Number

Every book that is cataloged in the National Library has an ________; it is consisting of 13 digits

4 colors, Four Color Theorem

Every planar graph is ____ colorable

William Rowan Hamilton (1805-1865, Irish)

Irish mathematician who studied "Hamiltonian" circuits

Floor Function

Is related to modulo function; we determine the quotient of two numbers and ignore the remainder. ( We don't round off)

Euler Circuit

It is a circuit/cyle where each edge in a graph is transversed once and starts and ends at the same vertex.

Hamiltonian Circuit

It is a cycle where the each vertex is traversed exactly once and starts and ends at the same vertex.

Weighted Graph

It is a graph where each edge is associated with a value called weight.

Halmiltonian Path

It is a path where each vertex is traversed exactly once and starts and ends at the different vertices.

Greedy Algorithm

It is an algorithm that finds a solution to problems in the shortest time possible. It makes us choose the cheapest option at every chance we get.

Chromatic Number of A Graph

It is the minimum number of colors needed to color a graph so that no edge connects vertices of the same color.

Luhn Algorithm

It is used to determine whether a credit card number is valid.

Degree of a vertex

It refers to the number id edges that is incident at a vertex (Number of Edge connected to a vertex.

Edge Picking Algorithm

The edge-picking algorithm gave the more efficient route.

Congruence

The statement a≡b mod n is called a, where n is a natural number, if (a-b)/n is an integer

True

True or False: Adding the modulus to a number does not change the value and can generate another congruence.

True

True or False: In general, there is no efficient method of finding the chromatics number of a graph

Next group of Digits

What digit of ISBN indicates the title of the book?

Euler Path Theorem

a connected graph has an Euler path if and only if it has two odd vertices with all other vertices of even degree.

Eulerian Graph Theorem

a connected graph is Eulerian if and only if every vertex of the graph is of even degree. Furthermore, the graph is Eulerian if it has the Euler Circuit

Connected Graph

a graph such that there is a path going from any vertex to any other vertex or connects two vertex sets

Disconnected Graph

a graph that is not connected; it has two or more connected components, if there is no path to connect two vertex sets.

Bipartite Graph

a graph that is possible to divide all its vertices into two disjoint subsets such that every edge in the graph connects a vertex in one subset to a vertex in the other subsets

Simple Graph

a graph with no loops or multiple edges

Modulo n

a mathematical operation that returns the remainder after integer division. Example: 7 MOD 4 = 3

Credit Card Numbers

are normally 13 to 16 digits long o The first one to four digits are used to identify the card issuer

First Digit; d1

composed of 978 (ISBN) what digit?

d13; last digit

digit of ISBN called check digit.

Path

in a graph it is a sequence of edges which joins a sequence of distinct vertices

Graph Theory

is a branch of mathematics which illustrates and analyzes connections between objects

UPC; Universal Code Product

is a number placed on many items and is particularly useful in grocery.; gives the store manager accurate information about inventory and the buying habits of the store ' s customers; is a 12-digit number that satisfies a congruence equation that is similar to the one for ISBNs

Graph

is a set of points called verices and line segments of curves called edges

Modular Arithmetic

is also called as "clock arithmetic". In real life, this idea can also be used to deal with "time" in terms of a 12-hour clock .

Loop

is an edge, the endpoint of which are the same vertex

Circuit

it is a closed path/cycle where a path ends at the same vertex at which it started

Null graph

it is a graph in which no edge is drawn between any two vertices

Directed graph

it is a graph where all the edges are directed from one vertex to another. It is also called a digraph

Complete Graph

it is a graph which every possible edge is drawn between the vertices

Euler Path

it is a path where each edge is a graph is transversed once and starts and ends at a different vertex

Graph Coloring

it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints

adjacent edge

two edge are ________ if they share a common vertex

equivalent graph

two or more graphs are equivalent if the edges form the same connections of vertices

adjacent vertices

two vertices are _______ if they share a common edge.

Next two to seven digits

what digit of ISBN indicates the publisher?