Discussion on some interesting topics in graph theory pdf

The discussion section should cover the following points, but note that for some. For those readers who desire a more extensive discussion of the history and solution of the four color problem, we recommend the interesting. Caldwell a series of short interactive tutorials introducing the basic concepts of graph theory, designed with the needs of future high school teachers in mind. Reinhard diestel graph theory 5th electronic edition 2016 c reinhard diestel this is the 5th ebook edition of the above springer book, from their series graduate texts in mathematics. Many problems in graph theory involve some sort of colouring, that is, assignment of labels or colours to the edges or vertices of a graph. Vaidya department of mathematics saurashtra university, rajkot 360 005 india. We also study directed graphs or digraphs d v,e, where the edges have a direction, that is, the. Graph theory is a very popular area of discrete mathematics with not only numerous theoretical developments, but also countless applications to practical problems. Graph theory, branch of mathematics concerned with networks of points connected by lines. Remember to always ask follow up questions to find out more. In this short introductory course to graph theory, possibly one of the most propulsive areas of contemporary mathematics, some of the basic graph theoretic concepts together with some open problems in this scientific field are presented. My registration was done in the year 2008 for carrying out the work related to the subject. See glossary of graph theory terms for basic terminology examples and types of graphs. The geometry of the vertex placement, or the contours of the edges are irrelevant.

Projects january 23, 2012 i chose these projects because i think they are all interesting. This paper is an exposition of some classic results in graph theory and their applications. Rather, i hope to use graph theory as a vehicle by which to convey a sense of developing advanced mathematics remember, these students will have seen firstyear calculus, at best. What are the current areas of research in graph theory. Some of these are quite heavy and some can be a bit of a downer, so make sure your conversation.

The closeness of the link between network analysis and graph theory is widely recognized, but the nature of the link is seldom discussed. A graph g is said to admit a triangular sum labeling if its vertices can be labeled by nonnegative integers. My registration was done in the year 2008 for carrying out the work related to the. Topics in algebraic graph theory the rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory. When it comes to creating a good powerpoint presentation, choosing an interesting topic can define your success. Not only do we want to introduce you to many of the interesting topics in this area of mathematics, but it is our desire to give you an idea of how these topics. Chapter 0 provides some background on the origin of graph colorings primarily giving a discussion of the four color problem.

A proof of tuttes theorem is given, which is then used to derive halls marriage theorem for bipartite graphs. Debate is competitive in nature while group discussion is a cooperative group process. What are you favorite interesting and accessible nuggets of graph theory. The topic of this volume is the connection between graph theory and algebra. It gives you everything you need to know to be prepared. An interesting feature of many problems in graph theory. Once people hit college, they have a pretty good idea about how the world works and should have some set beliefs and standards based on what they believe to be moral or immoral. Discussion on some interesting topics in graph theory reference. Graph theory goes back several centuries and revolves around the study of graphs. After considerable development, the tools they used in this paper led. Author gary chartrand covers the important elementary topics of graph theory. In a debate, a speaker can speak either for the topic or against the topic. Heres a course on effective public speaking and interesting topics. The traditional way to associate a graph to a group g and a set s of generators.

There are links with other areas of mathematics, such as design theory. There is a part of graph theory which actually deals with graphical drawing and presentation of graphs. References 160 62m a seoud and m z youssef, on harmonious graphs of order 6, ars combin. In this short introductory course to graph theory, possibly one of the most propulsive areas of contemporary mathematics, some of the basic graph theoretic concepts together with some. Graphs and their cartesian product is a scholarly textbook of graph theory. This tutorial offers a brief introduction to the fundamentals of graph theory. What makes information spaces such as the web interesting for our stud. There is a part of graph theory which actually deals with graphical drawing and presentation of graphs, brie. Well, you can expect most of the topics taught in graph theory here in subsequent articles. Chapters cover cartesian products, more classical products such as hamiltonian graphs, invariants, algebra and other topics. Also present is a slightly edited annotated syllabus for the one. Here we discuss a method based on an interesting graphtheoretic lemma. A few solutions have been added or claried since last years version. Rob beezer u puget sound an introduction to algebraic graph theory.

Tutte on the occasion ofhis sixtieth birthday, university of waterloo, july 59, 1977. Pdf in this short introductory course to graph theory, possibly one of the most. Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics. Which seemed to me to be herculean task ab initio but with the passing of time, everything seemed to be within the reach by gods grace. The subject of graph theory had its beginnings in recreational math problems see number game. I have done some topics related to both graph theory as a point of view of doing it as a mathematics student and also studied some graph algorithms. Some applications of eulerian graphs 3 thus a graph is a discrete structure that gives a representation of a finite set of objects and certain relation among some or all objects in the set. There are numerous instances when tutte has found a beautiful result in a hitherto unexplored branch of graph theory. Graph theory and related topics proceedings ofthe conference held in honour of professor w. Tree set theory need not be a tree in the graph theory sense, because there may not be a unique path between two vertices tree descriptive set theory euler tour technique. This is a list of graph theory topics, by wikipedia page. Written in a readerfriendly style, it covers the types of graphs, their properties, trees, graph traversability, and the.

For many, this interplay is what makes graph theory so interesting. The theory of graphs is a branch of discrete mathematics which cuts across wide. Ustimenko, on some optimization problems on graphs and cryptography on many variables. It would be tough for us to visit all available problems in graph theory, but we will be taking up several interesting. Therefore, the discussion section will generally need to include references. You can scan the topics to see what interests you or just choose a topic at random and get started.

Written in a readerfriendly style, it covers the types of graphs, their properties, trees, graph traversability, and the concepts of coverings, coloring, and matching. Discussion on some interesting topics in graph theory a thesis submitted to saurashtra university rajkot for the award of the degree of doctor of philosophy. Before leading the say it out loud youth discussion group, here are things you can do to prepare and to help ensure that it is a success. In the present work we investigate some classes of graphs which does not admit a triangular sum labeling. Discussion on some interesting topics in graph theory in the subject of mathematics. Projects october 11, 2008 i chose these projects because i think they are all interesting. Introductory graph theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Discussion on some interesting topics in graph theory a thesis submitted to saurashtra university rajkot for the award of the degree of doctor of philosophy in mathematics by prakash l. Discussion the purpose of the discussion section is provide an explanation for your results and to interpret those results in the context existing theory and knowledge. Both teachers and students get bored with dull presentation topics. For a more detail discussion on group actions we refer the.