# Author: dharam

## Hamiltonian Circuit – Seating Arrangement Problem

Here is a problem statement "Twenty members of a club meet each evening for dinner at a round table. They plan to sit such that every member has different neighbors every evening. Find out the number of days for which this arrangement can last." Here is another one "There is a list of 20 cities with roads connecting them, a salesman wants to sell his goods by visiting each city exactly once. Is that possible for a given network of cities?" Many a times we have been given problems like above and it is not really easy to solve them if we are not equipped with the Graph Theory. What ...

## Euler Graphs – Origin of Graph Theory

This should have been my first post in the Graph Theory series but nevertheless I got time to discuss this now. Every one must have heard the famous problem of Seven Bridges of Königsberg. If not, then please take some time to read about the problem either on the Wikipedia or right down below: The city of Konigsberb is located on both the banks of the river Pregel(Kaliningrad, Russia - former Prussia).  The city also included two big islands and these islands were connected to each other and the main land by the means of seven bridges. Something like below: The problem is to devise a...