Quartic Circulant graph notation example I would like to ask. I found the original image from Wolfram website and then cropped this example of circulant graph. Source:
https://mathworld.wolfram.com/QuarticGraph.html
Why does it says it is circulant graph (1,2)? Should not it be (1,5)?
I am new to graph theory, so would like to make sure, and I dont see in google about that notation also.
Thanks in advance.

 A: The picture is "correct", but it is drawn very confusingly, and you are right to be suspicious. The clearer version of the picture would have an 11-cycle around the outside, with an edge between every pair distance 2 on the cycle (which is what I think you were expecting to see).
The vertices of distance $1$ apart are connected by the long, diagonal edges. In particular, these form a cycle of length 11. The vertices distance $2$ apart (as in, distance two apart on the cycle formed by the long edges) are connected by short edges. So it is $C(1,2)$.
EDIT: The notation works like this. The $n$-Circulant graph $C(a_1, a_2, \dots, a_k)$ has vertex set $\{0,1,2,3,\dots, n-1\}$. You make two vertices $i$ and $j$ adjacent whenever the difference $|i-j| = a_m \pmod n$, for some $a_m$ in $\{a_1, a_2, \dots, a_k\}$.
So in this example, your vertex set is $\{0, 1, \dots, 10\}$, and any time two vertices differ by either $1$, or $2$, modulo $11$, you make them adjacent.
A: One of the definitions of a circulant graph:
The graph is a Cayley graph of a cyclic group.
For example, $\operatorname{Cay}(\mathbb{Z}_n;a_1,\ldots,a_r)$ is a Cayley graph of $\mathbb{Z}_n$
with the set of generators consisting of elements
$\{a_1,\ldots,a_r\}$.
Thus the $11$-circulant graph $(1,2)$ is the $\operatorname{Cay}(\mathbb{Z}_{11};1,2)$,
similarly the $11$-circulant graph $(1,5)$
is $\operatorname{Cay}(\mathbb{Z}_{11};1,5)$.
Since $\operatorname{Cay}(\mathbb{Z}_{11};1,2)\cong \operatorname{Cay}(\mathbb{Z}_{11};1,5)$
(the second graph is obtained from the first one by multiplication by $5$),
of course we can assume that the picture shows both mentioned graphs.
