Network Notes Ms Allan 2012 AS91260 (2.5) Designed to teach from,

Slides:

Advertisements

Similar presentations

Clever Counting Investigation 3. Making Rounds A. How many paths are there from A to B? How many paths are there from B to C? B. How many paths are there.

Advertisements

A Triangle given the 3 sides

1 Counting Perfect Matchings of a Graph It is hard in general to count the number of perfect matchings in a graph. But for planar graphs it can be done.

Analysis of Algorithms Depth First Search. Graph A representation of set of objects Pairs of objects are connected Interconnected objects are called “vertices.

EMIS 8374 Vertex Connectivity Updated 20 March 2008.

AB 11 22 33 44 55 66 77 88 99 10  20  19  18  17  16  15  14  13  12  11  21  22  23  24  25  26  27  28.

Module 5 – Networks and Decision Mathematics Chapter 24 – Directed Graphs.

Pamela Leutwyler. A river flows through the town of Konigsburg. 7 bridges connect the 4 land masses. While taking their Sunday stroll, the people of Konigsburg.

Decision Maths Graphs Wiltshire Graphs A graph is just a diagram made up of “dots” and “lines”. These are all graphs. The dots are called “nodes” or.

1 Representing Relations Part 2: directed graphs.

(a) (b) (c) (d). What is (1,2,3)  (3,4,2)? (a) (1, 2, 3, 4) (b) (1,2)  (3,4) (c) (1,3,4,2) (d) (3,1)  (4,2)

The Bridge Obsession Problem By Vamshi Krishna Vedam.

Chinese postman problem

Can you connect the dots as shown without taking your pen off the page or drawing the same line twice.

Euler and Hamilton Paths. Euler Paths and Circuits The Seven bridges of Königsberg a b c d A B C D.

Chapter 2: Graphs and Networks Lesson 2: Hello Mr Euler…

SWBAT find the measure of an inscribed angle. P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than.

EXAMPLE 1 Standardized Test Practice SOLUTION Let ( x 1, y 1 ) = ( –3, 5) and ( x 2, y 2 ) = ( 4, – 1 ). = (4 – (–3)) 2 + (– 1 – 5) 2 = = 85 (

Graph Theory. A branch of math in which graphs are used to solve a problem. It is unlike a Cartesian graph that we used throughout our younger years of.

. Now try this one Challenge:  Is this even possible?  One gets stuck….

Graph theory and networks. Basic definitions  A graph consists of points called vertices (or nodes) and lines called edges (or arcs). Each edge joins.

Chapter 6: Graphs 6.1 Euler Circuits

Review Euler Graph Theory: DEFINITION: A NETWORK IS A FIGURE MADE UP OF POINTS (VERTICES) CONNECTED BY NON-INTERSECTING CURVES (ARCS). DEFINITION: A VERTEX.

Geometry Chapter 1.

1.3 Segments and Measure The segment postulate Distance Formula.

15B Critical path analysis. In a critical path analysis, edges represent activities. Nodes (vertices) represent the end of one activity and the start.

Graphs Definition: a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected.

Chapter Chapter Summary Graphs and Graph Models Graph Terminology and Special Types of Graphs Representing Graphs and Graph Isomorphism Connectivity.

CSC 172 DATA STRUCTURES.

Basic Concepts Graphs For more notes and topics visit:

Graph Graphs and graph theory can be used to model:

Calculus with Parametric Curves

Algebra substitution.

Discrete Structures – CNS2300

Warm up! Find the perimeter of the shaded region.

Graphs and Graph Models

تصنيف التفاعلات الكيميائية

Spanning Trees Discrete Mathematics.

CSC 172 DATA STRUCTURES.

Introduction to Graph Theory Euler and Hamilton Paths and Circuits

Lecture 15: Graph Theory II

<APB is a Central Angle

Factoring Foundation Ms. Finnegan Algebra 1.

A Triangle given the 3 sides

Konigsberg- in days past.

Route Inspection The first method mark is for three distinct pairings of the correct four odd nodes. Get this wrong and you lose all say (five) marks.

Objectives The student will be able to:

Bell Ringer 10/27/10 What is the GCF? 18x³y² and 24x² ab and a³b².

AB AC AD AE AF 5 ways If you used AB, then, there would be 4 remaining ODD vertices (C, D, E and F) CD CE CF 3 ways If you used CD, then, there.

Decision Maths Graphs.

Route Inspection Which of these can be drawn without taking your pencil off the paper and without going over the same line twice? If we introduce a vertex.

Reading: ‘Washington, DC’

Euler and Hamilton Paths

GRAPHS G=<V,E> Adjacent vertices Undirected graph

Networks Prim’s Algorithm

Factoring using the greatest common factor (GCF).

Multiplying integers 3(3) = (3) = (3) = (3) = 0 -3

Warm Up – 3/19 - Wednesday Give the vertex set. Give the edge set.

Inscribed Angles & Inscribed Quadrilaterals

Chapter 10 Graphs and Trees

Betweenness, Segments and Rays, Point-Plotting Thereom

Weighted Graphs AQR.

Warm Up – 3/17 - Monday A) List the set of vertices.

Objectives The student will be able to:

For Friday Read chapter 9, sections 2-3 No homework

Vertex Covers and Matchings

Let’s review ?.

Presentation transcript:

Network Notes Ms Allan 2012 AS91260 (2.5) Designed to teach from, Not as complete notes.

ABC and D are Nodes or Vertices

BC is an arc, edge or path

There are two arc, edge or paths between A and B There are two arc, edge or paths between A and B. Lets call them AB1 and AB2.

A has two arcs: it is an even Node.

B has 6 arcs, it is an even Node.

All Nodes are even => Traversable.

Node B has 7 arcs: it is an odd node Node B has 7 arcs: it is an odd node. Node C has 5 arcs: it is an even node.

This network has Exactly 2 odd nodes: It is traversable starting at one odd node and ending at the other odd node.

More than 2 odd nodes? Not traversable!