discrete mathematics with graph theory 3rd edition pdf free download

For now, notice how we would ask this question in the context of graph theory. Is it possible to do this without any of the utility lines crossing? We will answer this question later. Each of three houses must be connected to each of three utilities.

That is, two vertices will be adjacent there will be an edge between them if and only if the people represented by those vertices are friends. Each person will be represented by a vertex and each friendship will be represented by an edge. It turns out that Al and Cam are friends, as are Bob and Dan.Įuler is friends with everyone. But first, here are a few other situations you can represent with graphs. We will return to the question of finding paths through graphs later. All that matters is which land masses are connected to which other land masses, and how many times.

It does not matter how big the islands are, what the bridges are made out of, if the river contains alligators, etc. The nice thing about looking at graphs instead of pictures of rivers, islands and bridges is that we now have a mathematical object to study. When two vertices are connected by an edge, we say they are adjacent. Graphs are made up of a collection of dots called vertices and lines connecting those dots called edges. MA8351 Notes Discrete Mathematics Regulation 2017 Anna University Pictures like the dot and line drawing are called graphs. Is it possible to trace over each line once and only once without lifting up your pencil, starting and ending on a dot? There is an obvious connection between these two problems. Are you? Graph Theory is a relatively new area of mathematics, first studied by the super famous mathematician Leonhard Euler in Since then it has blossomed in to a powerful tool used in nearly every branch of science and is currently an active area of mathematics research. As time passed, a question arose: was it possible to plan a walk so that you cross each bridge once and only once?Įuler was able to answer this question. The bridges were very beautiful, and on their days off, townspeople would spend time walking over the bridges. The islands were connected to the banks of the river by seven bridges as seen below.

Discrete mathematics with graph theory 3rd edition pdf free download