Answer to Question #201560 in Discrete Mathematics for Kavin Mahendran

Question

1. Assess whether the following undirected graphs have an Eulerian and/or a Hamiltonian cycle. 

Answer 1

An Euler cycle is a cycle that uses every edge of a graph exactly once.

If a graph G has an Euler cycle, then all of its vertices must be even vertices.

If the number of odd vertices in G is anything other than 0, then G cannot have an Euler cycle.

Euler cycle: CDEBBADC

A Hamiltonian cycle is a cycle that visits every vertex once with no repeats. Being a cycle, it must start and end at the same vertex.

The given graph has not Hamiltonian cycle.