a)The graph has an Euler circuit : a,b,c,d,e,g,c,h,e,f,h,b,f,a .

b)It doesn't have a Hamilton circuit . Because :

A Hamilton circuit is the longest circuit .

It never contains other circuits. (1)

It always contains every edges next points x that d(x) = 2 . (2)

If having a Hamilton circuit ,the Hamilton will contains eg , gc , cd and ed (2) . But these 4 edges create a circuit . Arcording to (1) , there is a conflict .

So , the graph has no a Hamilton circuit .