Consider the graph G below Is G a simple graph Why or why no

Consider the graph G below: Is G a simple graph? Why or why not? Does G have an Eulerian Circuit? Find one that starts and ends at A or explain why none exists. Does G have a Hamiltonian circuit? If so find one that starts and ends at A or explain why none exists.

Solution

Solution : a) Given graph is simple graph because it does not contains any loop or multiple ages.

b) All of the vertices have even degree except B (degree 5) and D (degree 3). According to Euler\'s Theorems, there is no Euler circuit for this given graph. (However, there is an Euler path, starting at one of the odd vertices and ending at the other)

C ) There is a Hamilton circuit ABCDGA.