A Graph theory question in discrete mathematics

[wintry bear]

Graph theory problem

[ruby dock]

To prove that if two graphs are isomorphic, then they have the same order, is it enough to state that by definition, there is a bijection between the sets of vertices $V_1$ and $V_2$ of graphs $G_1$ and $G_2$, therefore $V_1$ and $V_2$ have the same cardinality?

[wintry bear]

A Graph theory question in discrete mathematics

[slow saddle]

herrperson

[sudden crater]

Yes, it's always the case that isomorphic graphs have the same numbers of vertices (and the same number of edges).