For any two directed graphs

G

$=$

$($

V

G

$,$

E

G

$)$

and

H

$=$

$($

V

H

$,$

E

H

$)$

$,$ define graph

G

$\backslash$times

H

$=$

$($

V

G

$\backslash$times

H

$,$

E

G

$\backslash$times

H

$)$

as follows:

there is a node in

G

$\backslash$times

H

for every pair of nodes from

G

and

H

$,$ formally:

V

G

$\backslash$times

H

$=$

V

G

$\backslash$times

V

H

$=$

$\{$

$($

v

G

$,$

v

H

$)$

:

v

G

in

V

G

$,$

v

H

in

V

H

$\}$

edges in

G

$\backslash$times

H

link pairs that are also themselves adjacent in the underlying

G

and

H

:

E

G

$\backslash$times

H

$=$

$\{$

$($

$($

u

G

$,$

u

H

$)$

$,$

$($

v

G

$,$

v

H

$)$

$)$

:

$($

u

G

$,$

v

G

$)$

in

E

G

$,$

$($

u

H

$,$

v

H

$)$

in

E

H

$\}$

Carefully consider the following graphs

G

and

H

: