Hello could you please help me with this question Given the

Hello, could you please help me with this question?

Given the graph below,   

a ) Is it simple?           Yes   ___       No __

b ) Is it connected?      Yes ___     No ___

c ) Is there an Euler path?     Yes ___        No ___

               d) Is there a Hamiltonian circuit?     Yes ___    No

Solution

a) YES. The given graph is simple because it has no loops and no multiple edges.

b) YES. The graph is connected because any two vertices of it are joined by atleast one path.

c) NO. because it has more than two vertices of odd degree and a graph with more than two vertices of odd degree can not have an Eulerian path.

d) YES