Answer
there is no such graph.
Work Step by Step
. If there were a graph with four vertices of degrees 1, 2, 3,
and 3, then its total degree would be 9, which is odd. But
by Corollary 10.1.2, the total degree of the graph must be
even. [This is a contradiction.] Hence there is no such graph.
(Alternatively, if there were such a graph, it would have
an odd number of vertices of odd degree. But by Proposition
10.1.3 this is impossible.)
