The melrose math circle mathematical association of america. Part5 practice problem on hand shaking theorem or sum. Download cs6702 graph theory and applications lecture notes, books, syllabus parta 2 marks with answers cs6702 graph theory and applications important partb 16 marks questions, pdf books, question bank with answers key. I strongly advise all students to print the complete set of pdf notes as we go along. Graph theory is a branch of mathematics, first introduced in the 18th century, as a way to model a puzzle. It gives a necessary and sufficient condition for being able to select a distinct element from each set. Request segment consists only of tcp header with an empty payload. For many, this interplay is what makes graph theory so interesting. A way of incorporating the problem into a history context is effectively shown on nctms illuminations website, which discusses the tradition of the supreme court justices all shaking hands with one another before each session. In graph theory, handshaking theorem or handshaking lemma or sum of degree of vertices theorem states that sum of degree of all vertices is twice the number of edges contained in it. That couple has multiplicities 5,1 in the full graph. The degree of a vertex is the number of edges incident with it a selfloop joining a vertex to itself contributes 2 to the degree of that vertex. Before three way handshake, both client and server are in closed state. If every vertex is adjacent to some other vertex, then is the graph connected.
Ulman acknowledge that fundamentally, computer science is a science of abstraction. Although very simple to prove, the handshaking lemma can be a powerful. In the course of the problems we shall also work on writing proofs that use mathematical. Cs6702 graph theory and applications notes pdf book. Is my induction proof of the handshake lemma correct. The descriptions of the lectures below are only help you identify the lecture you seek. Suppose you and your spouse attend a party with 3 other couples. The concept of graphs in graph theory stands up on some basic terms such as point, line, vertex, edge, degree of vertices, properties of graphs, etc. Ramsey theory fortwographsgandh,letrg,h denotethe smallestintegermsatisfying the property that if the edges of the complete graph km are colored in blue and. Reinhard diestel graph theory electronic edition 2000 c springerverlag new york 1997, 2000 this is an electronic version of the second 2000 edition of the above springer book, from their series graduate texts in mathematics, vol. H discrete mathematics and its applications, 5th ed. Because every handshake increases the total degree by 2. I first heard about it in an algebra course i took in high school, and its stuck with me through the years.
Data modelling with graph theory part 1 introduction. How would you solve this graph theory handshake problem in. Graph theory is a natural abstraction for many atm problems used known graph problems to learn about atm problem polynomial transformation can be used to gain insights about inherent difficulty of new problems solve new problems efficiently linking problems allows. Acta scientiarum mathematiciarum deep, clear, wonderful.
Computer scientists must create abstractions of realworld problems. And of course you must have multiplicity x3 so your husband shook 3 hands. Handshakes and graphs and ramsey theory warmup problems. If the graph has an eulerian path, then solution to the problem is the euler path and the shortest return path to the starting point. Unfortunately, when i try to simulate a smaller problem with 3 couples, i am getting that each couple is shaking 4 hands. Acknowledgement much of the material in these notes is from the books graph theory by reinhard diestel and introductiontographtheory bydouglaswest. We will now look at a very important and well known lemma in graph theory. Cs 7 graph theory lecture 2 february 14, 2012 further reading rosen k. In particular, the n choose 2 formula, which serves as the basis of the handshake puzzle, is a fundamental concept in probability that can be used to compute a wide range of mathematical problems, as will be demonstrated in this workshop. If everyone in a group shakes hands, how many total handshakes are. Contents 1 introduction 3 2 notations 3 3 preliminaries 4 4 matchings 5 connectivity 16 6 planar graphs 20 7 colorings 25 8 extremal graph theory 27 9 ramsey theory 31 10 flows 34 11 random graphs 36 12 hamiltonian cycles 38 references 39. We are very thankful to frank for sharing the tex les with us. Handshakes puzzle graph theory problem symmetric relation. Graph theory, branch of mathematics concerned with networks of points connected by lines.
Introduction to graph theory allen dickson october 2006 1 the k. Some problems in graph theory and graphs algorithmic theory. The handshake problem and graph theory session ii four color theorem. In graph theory, a branch of mathematics, the handshaking lemma is the statement that every finite undirected graph has an even number of vertices with odd degree the number of edges touching the vertex. In this paper, we ll in the mathematical details necessary for a full and complete description of our theory. The handshake problem tamisha is in a geometry class with 25 students. There is a part of graph theory which actually deals with graphical drawing and presentation of graphs, brie. In mathematics, halls marriage theorem, proved by philip hall, is a theorem with two equivalent formulations. This is such an attractive way of understanding the situation that the following theorem is often called the handshake lemma or the handshake theorem. How to graphically represent permutation problem a. Therefore, it is important to discuss basic notions from graph theory. Given a bipartite graph with sides a and b, we say that a subset c of b is smaller than or equal in size to a subset d of a in the graph if there exists an injection in the graph namely, using only edges of the graph from c to d. Each person is a vertex, and a handshake with another person is an edge to that person.
Thus, the number of vertices with an odd degree is even. Assume that a complete graph with kvertices has kk 12. There are no standard notations for graph theoretical objects. Jun 20, 2018 this is part 1 of 3 about using graph theory to interact with data. The elements of v are called vertices and the elements of eare called edges.
Lecture notes on graph theory budapest university of. The handshake problem has many variations in presentation. Among any group of 4 participants, there is one who knows the other three members of the group. The game is called sprouts and it is an invention of john horton conway. Theorem of the day the handshaking lemma in any graph the sum of the vertex degrees is equal to twice the number of edges. The handshaking lemma in any graph the sum of the vertex degrees is. Brainstorm some ways that you could use to find an answer to tamishas question.
In the other cases, solving the problem of mail delivery involves to designate. Part5 practice problem on hand shaking theorem or sum of degree theorem. Part5 practice problem on hand shaking theorem or sum of. Tcp handshake involves the following steps in establishing the connection step01. Eulers famous 1736 analysis of the bridges of konigsberg problem. For example, it shows up in airline scheduling, communications, computer programming, circuit design, the analysis of chicken pecking orders, etc. Tamisha wants to know how many handshakes had just been exchanged. Verify spatial visualization is a critical skill for mathematical understanding.
So as you iterate through the process you will conclude your couples have multiplicities 6,0, 5,1, 4,2, 3,3. There is exactly one person who shakes hand with an odd number of persons. Notice that the puzzle, as adjusted to ignore one handshake on the part of each person at the party, is identical to the original puzzle. Graphs are excellent at creating simplified, abstract models of problems. The dots are called nodes or vertices and the lines are called edges.
Shake hands with some people you havent talked to in the past few. Network theory provides a set of techniques for analysing graphs. Math 215 project number 1 graph theory and the game of sprouts this project introduces you to some aspects of graph theory via a game played by drawing graphs on a sheet of paper. The marriage theorem does extend to the infinite case if stated properly. In every finite undirected graph number of vertices with odd degree is always even. These four regions were linked by seven bridges as shown in the diagram. When we use some terms of graph theory to think of this question, we can consider a vertex and an edge as a person and a handshake respectively. I proof is by induction on the number of vertices n. I decided to taught myself some basic graph theory and i tried to prove the handshake lemma using induction. A discrete mathematical model for solving a handshaking.
Prove that any complete graph k n has chromatic number n. Math 215 project number 1 graph theory and the game. Show that an even number of people shake hands an odd number of times. Degree of a vertex, regular graph, even and odd vertex, defined. Prove that there is one participant who knows all other participants. A graph is a diagram of points and lines connected to the points. The diagram below is a graph that has a bearing on the problem. In more colloquial terms, in a party of people some of whom shake hands, an even number of people must have shaken an odd number of other peoples hands. Jan 22, 2014 how to graphically represent permutation problem a. Discrete mathematics introduction to graph theory 1234 2. Part4 handshaking theorem in graph theory in hindi or sum of degrees of vertices theorem in hindi duration. The melrose math circle our intention is to have an experience that is. Reflecting on the handshake problem national council of.
A graph is a set of points, called vertices, together with a collection of lines, called edges, connecting some of the points. The handshaking lemma is a consequence of the degree sum formula also sometimes called the handshaking lemma how is handshaking lemma useful in tree data structure. Syn for establishing a connection, client sends a request segment to the server. Spresser department of mathematics and computer science james madison university, harrisonburg, virginia 22807 usa abstract. So im having trouble with this problem i have for homework. Practice problem on hamiltonian graphs euler graphs in hindi how to find identify. Graph theory was born in 1736 when leonhard euler published solutio problematic as geometriam situs pertinentis the solution of a problem relating to the theory of position euler, 1736.
Graph theory and the handshake problem the handshake problem the handshake problem is something of a classic in mathematics. We map the problem at hand patching together isolated k p expansions into consistent global band structures to a tractable problem in graph theory. Many of them were taken from the problem sets of several courses taught over the years. He presented a solution to the bridges of konigsberg problem in 1735 leading to the definition of an euler path, a path that went over each road exactly once. Euler euler path euler was a swiss mathematician, physicist, astronomer and engineer. The graph obtained by deleting the edges from s, denoted by g s, is the graph obtained from g by removing all the edges from s. You figured that one couple has multiplicities 6,0. Wilson, graph theory 1736 1936, clarendon press, 1986.
Handshake the sum of the degrees is twice the number of edges. Handshaking lemma and interesting tree properties geeksforgeeks. The combinatorial formulation deals with a collection of finite sets. In general, this problem concerns of travelling in a graph such that one tries to avoid usingany edge twice. Cs6702 graph theory and applications notes pdf book anna university semester seven computer science and engineering slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. The master of trinity college and his wife invite n fellows and their wives to a party. Here is the graph model of the problem a graph is a set of points we call them vertices or nodes connected by lines edges or arcs. During the party a fellow may shake hands with anyone except himself and his wife assume all fellows are male, and that theyll only shake hands with someone once. One by one, the largest handshaker and his or her spouse, the smallest handshaker, are removed from the puzzle until only the master and his wife remain. Since one edge is incident with 2 vertices note that g is simple, we can easily see that 1 handshake consists of 2 people, that is, 2 hands. The river divided the city into four separate landmasses, including the island of kneiphopf.
Thinking strategies to enhance skills of analysis, creativity, and problem solving. If g v, e is a graph, a kvertexcoloring of g is a way of assigning. On the first day of class her teacher asks everyone to shake hands and introduce themselves to each other. It has at least one line joining a set of two vertices with no vertex connecting itself. If each of the people shakes hands exactly once with each of.
If a graph is connected, then every vertex must be adjacent to some other vertex. E consists of a nite set v and a set eof twoelement subsets of v. Every connected graph with at least two vertices has an edge. This outstanding book cannot be substituted with any other book on the present textbook market. Graph theory is a very important tool in many aspect of modern life. A graph h is a subgraph of a graph g if all vertices and edges in h are also in g.
The nice thing about this problem is you dont really need to solve the graph if you dont want to. The resulting graph is called the complete graph on 20 vertices. In our first example, we will show how graph theory can be used to debunk an. Prove that a complete graph with nvertices contains nn 12 edges. Berkeley math circle graph theory october 8, 2008 2 10 the complete graph k n is the graph on n vertices in which every pair of vertices is an edge. The subject of graph theory had its beginnings in recreational math problems see number game, but it has grown into a significant area of mathematical research, with applications in chemistry, operations research, social sciences, and computer science. Of course, no one shook their own hand or the hand of the person they came with. Pdf cs6702 graph theory and applications lecture notes. Suppose that vertices represent people at a party and an edge indicates that the people who are its end vertices shake hands. Share and explain verbalize record thinking during and after solving a problem. Many fields in mathematics have strong foundations in combinatorics such as graph theory, probability, and statistics. Show that if every component of a graph is bipartite, then the graph is bipartite.
Chinese postman problem if the graph is an eulerian graph, the solution of the problem is unique and it is an euler cycle. Then follows the handshake problem, which asks how many. The remainder of the vertices are undifferentiated from each other with respect to the first couple and you have the same rules for that subgraph. It has every chance of becoming the standard textbook for graph theory. The graph theoretic formulation deals with a bipartite graph. E where v is a set of vertices, and the edge set e is a set of 2element subsets of v.
Discrete mathematics introduction to graph theory 14 questions about bipartite graphs i does there exist a complete graph that is also bipartite. In the language of graph theory, we are asking for a graph1 with 7 nodes in. Graph theory ask question asked 5 years, 11 months ago. In particular, the n choose 2 formula, which serves as the basis of the handshake puzzle, is a fundamental concept in probability that can be used to compute a. Graph theory handshaking problem computer science stack. An introduction to graph theory evelyne smithroberge university of waterloo march 22, 2017. As you can see both a1 and a2 have 4 blue lines each that are attached ie they shake hands to the other couples. The bipartite matching problem is related to the sexinamerica problem that we. The situations in the warmup problems can be represented by graphs. If gis a graph we may write vg and eg for the set of vertices and the set of edges respectively. We interpret graph theory in the broad sense, for example, including hypergraphs and in. In more colloquial terms, in a party of people some of whom shake hands, an even number of people must have shaken an odd number of other. A problem was whether it was possible to take a walk through the town in such a way as to cross over every bridge once, and only once. This is a serious book about the heart of graph theory.