Define Euler Circuit and Euler Path.  Which of the following graphs have an Euler circuit and Euler path.  

Ans:  In a graph G, a path is known as an Euler path if it contains each edge of the graph exactly once. An Euler path that is circuit is known as an Euler circuit. In the following, for instance, (a) has an Euler path but no Euler circuit, (b) has both of the Euler circuit and Euler path whereas (c) has none.     

A graph G, comprising more than two vertices of odd degrees, does not possess an Euler path. As the given graph (i) and (ii) both consists of more than two nodes of odd degree, neither (i) nor (ii) has any Euler path or Euler circuit.