Allpossible vertical lines will cut this graph only once. The notes form the base text for the course mat62756 graph theory. In function notation, the parentheses do not mean multiplication. Lesson notes on whiteboard students copied these in their notebooks. Graphs of polynomial functions notes multiplicity the multiplicity of root r is the number of times that x r is a factor of px. Graph theory notes january 25, 2017 1 matrix tree theorem theorem 1 matrix tree theorem. A null graph is a graph with no vertices and no edges. A graph is a set of points, called vertices, together with a collection of lines, called edges, connecting some of the points. Half of the text of these notes deals with graph algorithms, again putting emphasis on networktheoretic methods. A subgraph is part of a graph, where we take some of its vertices and edges. A complete graph on n vertices is denoted kn, and is a simple graph in which every two vertices are adjacent. Vertexh hasdegree 1, d has degree 2, and e has degree 3. En on n vertices as the unlabeled graph isomorphic to n.
We note that this graph cannot be colored with less than four colors. 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. You can use the letter f to name this function and then use function notation to express it. However, not every rule describes a valid function.
Notes on graph theory logan thrasher collins definitions 1 general properties 1. A graph is the set of all the ordered pairs whose coordinates. Odd multiplicity the graph of px crosses the xaxis. Contents introduction 3 notations 3 1 preliminaries 4 2 matchings 12 3 connectivity 15 4 planar graphs 19 5 colorings 24 6. Introduction to functions mctyintrofns20091 a function is a rule which operates on one number to give another number. Each increment increases by 10 units on the yaxis xaxis and yaxis can have. Graph theory lecture notes 4 application minimum spanning tree. The directed graphs have representations, where the edges are drawn as arrows. Notes on graph theory maris ozols june 8, 2010 contents. A graph h is a subgraph of a graph g provided the vertices of h are a subset.
Color the edges of a bipartite graph either red or blue such that for each. A simple graph is a nite undirected graph without loops and multiple edges. A graph g can be colored here, we color vertices by. Cs6702 graph theory and applications notes pdf book anna university semester seven computer science and engineering. Show that if all cycles in a graph are of even length then the graph is bipartite. Page 1 of 2 graphing and evaluating functions many functions can be represented by an in two variables, such as y 2x. We also study directed graphs or digraphs d v,e, where the edges have a direction, that is, the edges are ordered. We were able to quickly create two different graphs using the same data because origin uses a. 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. Find materials for this course in the pages linked along the left. Example 2 graph y 5 abx 2 h 1 k for b 1 graph the function y 5 1 4 p 6x. Notes bipartite graphs theorem a graph is bipartite if and only if it contains no oddlength cycles. For example, in the graph above, a is adjacent to b and b isadjacenttod,andtheedgeac isincidenttoverticesaandc.
Contents 1 introduction 3 2 notations 3 3 preliminaries 4 4 matchings 5 connectivity 16 6 planar graphs 20 7 colorings 25 8. In this chapter well look at two very important topics in an algebra class. Cs6702 graph theory and applications notes pdf book. Sub graphs that do not even have vertices in common are said to be vertex disjoint. Notes on data and bar graph this photo is the complete set of notes just prior to graphing.
Basic concepts in graph theory the notation pkv stands for the set of all kelement subsets of the set v. Gse advanced algebra name september 25, 2015 standards. Suppose that the vertices of a graph represent towns and the edges of the graph are roads between these towns. The first question that we should ask is what exactly is a graph of an equation. First, we will start discussing graphing equations by introducing the cartesian or rectangular coordinates system. Notes on graph theory thursday 10th january, 2019, 1. This unit explains how to see whether a given rule describes a valid function, and introduces some of the mathematical terms associated with functions. More than any other field of mathematics, graph theory poses some of the deepest and most fundamental. Function notation the equation y 9 4x represents a function. 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. Cs6702 graph theory and applications 9 note that although edgedisjoint graphs do not have any edge in common, they may have vertices in common. Cs6702 graph theory and applications notes pdf book anna university semester seven computer science and engineering slideshare uses cookies to improve functionality and performance. Discrete mathematics and algorithms lecture 2 we repeat this procedure until there is no cycle left. They contain an introduction to basic concepts and results in graph theory, with a special emphasis put on the networktheoretic circuitcut dualism.
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