Are two graphs isomorphic? Are the two graphs isomorphic?
$$G_1=\begin{bmatrix}
a & b & c & d & e & f \\ 
b & a & a & c & d & a \\
c & c & b & e & f & d \\
f &   & d & f &   & e 
\end{bmatrix}\  
\quad\quad
G_2=\begin{bmatrix}
u & v & w & x & y & z \\ 
v & u & v & u & x & u \\
x & w & x & w & z & w \\
z &   & z & y &   & y 
\end{bmatrix}$$
$a,b,c$ creates a triangle in $G_1$, but no triangle is created in $G_2$.
Is that enough to claim that they are not isomorphic?

"Isomorphic" does not only mean that the (sorted) degree-sequences must coincide.
For every set of vertices in one graph there must be a corresponding set of vertices in the other graph with the property that two vertices in one set are connected if and only if the corresponding vertices in the other set are connected.
In short, every subgraph must occur also in the other graph, if they are isomorphic.
So, if one graph contains a triangle, quadrilateral, pentagonal and so on, but not the other, they cannot be isomorphic.
