Answer to Question #272684 in Discrete Mathematics for Asif

Question

4.      In Exercises i) and ii) determine whether the given graph has a Hamilton circuit. If it does, find such a circuit. If it does not, give an argument to show why no such circuit exists.

i)                    

ii)                 

Answer 1

Consider the graph below

There does not exist any Hamilton circuit.

The degree sequence of the graph is {4,4,3,4,4,3}

Since the graph has 2 vertices of odd degree, hence by Hamilton theorem it does not have a Hamilton circuit