What does the $\times$ mean in $C_4 \times C_3$ in graph theory?

Question

How does one $ \times $ $2$ graphs? I'm not exactly sure what it means.

Answer 1

This depends on the author of the book you're using. There isn't a universally agreed upon notation in Graph Theory. If you're using a Chartrand book, then chances are $\times$ denotes the Cartesian Product of a set of graphs.

For two graphs $G$ and $H$, the Cartesian Product $G\times H$ has vertex set $V(G\times H)=V(G)\times V(H)$, that is, every vertex of $G\times H$ is an ordered pair $(u,v)$, where $u\in V(G)$ and $v\in V(H)$. Two distinct vertices $(u,v)$ and $(x,y)$ are adjacent in $G\times H$ if either $(1)$ $u=x$ and $vy\in E(H)$ or $(2)$ $v=y$ and $ux\in E(G)$.