I was told isomorphism was when two graphs are the same but have different forms. In order for it to be the same two vertices must be adjacent across the graphs. So if vertex1 is adjacent to vertex2 and vertex3 in one graph, than it must do so in the other. Also that isomorphism can easily be applied to other varietys of graphs.
The simple graphs $G1 = (V_1, E_1)$ and $G2 = (V_2, E_2)$ are isomorphic if there exists a one-to-one and onto function $f:V_1\to V_2$ with the property that $a$ and $b$ are adjacent in $G_1$ if and only if $f(a)$ and $f(b)$ are adjacent in $G_2$, for all $a$ and $b$ in $V_1$. Such a function $f$ is called an isomorphism. ∗ Two simple graphs that are not isomorphic are called nonisomorphic.
Are these two graphs isomorphic? They retain the same shape, but the direction of the edge from vertex1 to vertex4 changes between the two, so it cant be isomorphic, right? Well, I was told it was without an explanation. Are they wrong, or am I missing something? Any help would be appreciated.