# Tips and Tricks for Solving the Exercises in Graph Theory with Applications by Bondy and Murty using the Solution Manual

PREREQUISITE: The catalog states that "admission to the math graduate program or permission" are the formal prerequisite. Students must have some background in proving theorems and a working knowledge of linear algebra, but all graph theory definitions will be covered and we will start from first principals of graph theory.

## solution manual of graph theory by bondy and murty 1

ABOUT THE COURSE: Graph theory is a relatively new area of math. It lies in the general area of "discrete math" (as opposed to continuous math, such as analysis and topology), along with design theory and coding theory. Historically, it is motivated by applied problems and still finds numerous applications, particularly in computer science (such as network design and the efficiency of algorithms). However, today it is a very vibrant area of pure mathematical research. ETSU has had a number of research graph theorists over the past several years, including Drs. Lawson, D. Knisley, Boland, Haynes, and Beeler (and, part-time, Godbole, Gardner, and Keaton). In this class we will survey graph theory, starting with first principles and definitions. So no background in graph theory is needed, but some background in proof techniques, matrix properties, and introductory modern algebra is assumed. Homework assignments will mostly involve the standard exercises in the text book, but will occasionally involve more advanced exercises. Some emphasis will be put on the research of those current ETSU faculty members involved in areas related to graph theory. In particular, some lectures will deal with graph (and digraph) decompositions, coverings, and packings. Automorphisms of graph (and digraph) decompositions will also be explored. We may have a few guest lectures given by my departmental colleagues on their area of research.A section of Graph Theory 2 (MATH 5450) will be offered in spring 2023, assuming there is an appropriate level of interest.

ACADEMIC MISCONDUCT: While I suspect that you may work with each other on the homework problems, I expect that the work you turn in is your own and that you understand it. Some of the homework problems are fairly standard for this class, and you may find proofs online or in an online version of the solutions manual. The online proofs may not be done with the notation, definitions, and specific methods which we are developing and, therefore, are not acceptable for this class. If I get homework from two (or more) of you that is virtually identical, then neither of you will get any credit. If you copy homework solutions from an online source, then you will get no credit. These are examples of plagiarism and I will have to act on this as spelled out on ETSU's "Academic Integrity @ ETSU" webpage (last accessed 7/20/2022). To avoid this, do not copy homework and turn it in as your own!!! Even if you collaborate with someone, if you write the homework problems out in such a way that you understand all of the little steps and details, then it will be unique and your own work. If your homework is identical to one of your classmates, with the exception of using different symbols/variables and changing "hence" to "therefore," then we have a problem! If you copy a solution from a solution manual or from a website, then we have a problem! I will not hesitate to charge you with academic misconduct under these conditions.