Ashton has invented a function $f$ that takes multigraphs as input values and returns integers as output values, defined
as follows:
For any multigraph $G$, we have $f(G) = |V(G)| \times |E(G)|$.
(a) Complete the following sentences:
The function $f$: {all graphs} $\to$ N is Click for List
The function $f$: {all connected graphs} $\to$ N is Click for List
Briefly justify your answers below.
(b) Ashton thinks that $f(K_{m,n})$ is even for all $m, n \in \mathbb{Z}^+$. Are they correct? Carefully prove your answer.
