The graph Cartesian product 
of a complete graph 
and a cycle
graph 
has been termed a "KC graph" by Knuth (2024, p. 22), who restricts
their parameters to 
and 
. The KC graphs are regular
with degree 
and have vertex count and edge
count
 |  |  |
(1)
|
 |  |  |
(2)
|
Special cases are summarized in the table below.
| graph | special case |
 | cycle graph  |
 | prism
graph  |
 | rook graph  |
 | generalized
quadrangle  |
for  | circulant
graph  |
is ungraceful
for 
odd (Knuth 2024, p. 22).
