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. This site does not host pdf, DOC files all document are the property of their respective owners.The islands were connected to the banks of the river by seven bridges as seen below.
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