A study of some aspects of random walk in graph theory

Graph theory is a fascinating subject. Its origin is as diverse as its applications. The Swiss Mathematician Leonard Euler (1707-1783) is clearly the father of graph theory. In the later of eighteenth century, he established an important result for a famous unsolved problem. It involved the seven bridges of Konigsberg, which connected two Islands and the banks of the river Pregel by seven bridges. The problem was to determine the route to walk across the seven bridges of Konigsberg, crossing each bridge only once and returning to the starting point. Euler proved this impossible and in doing so laid the foundation of graph theory.