Nnnfunction and graph notes pdf

A graph is the set of all the ordered pairs whose coordinates. In this chapter well look at two very important topics in an algebra class. A null graph is a graph with no vertices and no edges. Notes on graph theory maris ozols june 8, 2010 contents. Note in the previous example, that transferring a factor of 2, or even better, 4, from the 6 to the 25 makes it easier. The directed graphs have representations, where the edges are drawn as arrows. En on n vertices as the unlabeled graph isomorphic to n. Allpossible vertical lines will cut this graph only once. However, not every rule describes a valid function. All graphs in these notes are simple, unless stated otherwise. We also study directed graphs or digraphs d v,e, where the edges have a direction, that is, the edges are ordered. The fact that each number in the domain of f is assigned a unique number in the range of f, implies that the graph of f will satisfy the vertical line test. A graph h is a subgraph of a graph g provided the vertices of h are a subset. Contents 1 introduction 3 2 notations 3 3 preliminaries 4 4 matchings 5 connectivity 16 6 planar graphs 20 7 colorings 25 8.

Since c 3 1, the graph is obtained from that of fx x12 by stretching it in the ydirection by a factor of c 3. Notes on graph theory logan thrasher collins definitions 1 general properties 1. For example, in the graph above, a is adjacent to b and b isadjacenttod,andtheedgeac isincidenttoverticesaandc. You read fx as f of x, which means the output value of the function f for the input value x. This unit explains how to see whether a given rule describes a valid function, and introduces some of the mathematical terms associated with functions. A graph is a set of points, called vertices, together with a collection of lines, called edges, connecting some of the points. Graph theory notes january 25, 2017 1 matrix tree theorem theorem 1 matrix tree theorem. Notes on data and bar graph this photo is the complete set of notes just prior to graphing. Lesson notes on whiteboard students copied these in their notebooks. They contain an introduction to basic concepts and results in graph theory, with a special emphasis put on the networktheoretic circuitcut dualism. Notes on graph theory thursday 10th january, 2019, 1. An ordered pair x,y is a of such an equationif the equationis true when the values of x and y are substituted into the equation. The first question that we should ask is what exactly is a graph of an equation. Basic concepts in graph theory the notation pkv stands for the set of all kelement subsets of the set v.

Introduction to functions mctyintrofns20091 a function is a rule which operates on one number to give another number. Color the edges of a bipartite graph either red or blue such that for each. Page 1 of 2 graphing and evaluating functions many functions can be represented by an in two variables, such as y 2x. As we saw in the notes on relations, there is a onetoone correspondence between simple. Odd multiplicity the graph of px crosses the xaxis. We were able to quickly create two different graphs using the same data because origin uses a. More than any other field of mathematics, graph theory poses some of the deepest and most fundamental. We note that this graph cannot be colored with less than four colors. Cs6702 graph theory and applications notes pdf book anna university semester seven computer science and engineering. Cs6702 graph theory and applications notes pdf book. In function notation, the parentheses do not mean multiplication.

A simple graph is a nite undirected graph without loops and multiple edges. Stony brook green port orient point riverhead edges. Each increment increases by 10 units on the yaxis xaxis and yaxis can have. A graph ghas a 1factor if and only if qg s jsjfor all s vg, where qh is the number of odd order components of h. You can use the letter f to name this function and then use function notation to express it. Graphs of polynomial functions notes multiplicity the multiplicity of root r is the number of times that x r is a factor of px. Example 2 graph y 5 abx 2 h 1 k for b 1 graph the function y 5 1 4 p 6x. Half of the text of these notes deals with graph algorithms, again putting emphasis on networktheoretic methods.

Cs6702 graph theory and applications 9 note that although edgedisjoint graphs do not have any edge in common, they may have vertices in common. Function notation the equation y 9 4x represents a function. Graph theory lecture notes 4 application minimum spanning tree. Sub graphs that do not even have vertices in common are said to be vertex disjoint. Discrete mathematics and algorithms lecture 2 we repeat this procedure until there is no cycle left. The notes form the base text for the course mat62756 graph theory. A complete graph on n vertices is denoted kn, and is a simple graph in which every two vertices are adjacent. The graph of a quadratic function is a special type of. Notes bipartite graphs theorem a graph is bipartite if and only if it contains no oddlength cycles. Note that a very different plot is created using the same datasets. First, we will start discussing graphing equations by introducing the cartesian or rectangular coordinates system.