[On a class of Hamiltonian laceable 3-regular graphs][1], contains the definition of the brick product of even cycles, with figures showing examples.

> **Definition.** Let $m$, $n$ and $r$ be a positive integers. Let $C_{2n} = 0 1 2 \ldots (2n - 1) 0$ denote a cycle of order $2n$. The _$(m, r)$-brick-product of $C_{2n}$_, denoted by $C(2n, m, r)$, is defined in two cases as follows.
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> For $m = 1$, we require that $r$ be odd and greater than $1$. Then $C(2n, m, r)$ is obtained from $C_{2n}$ by adding chords $2k (2k + r)$, $k = 1, \dots, n$, where the computation is performed modulo $2n$.
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> For $m > 1$, we require that $m + r$ be even. Then $C(2n, m, r)$ is obtained by first taking the disjoint union of $m$ copies of $C_{2n}$, namely $C_{2n}(1), C_{2n}(2), \dots, C_{2n}(m)$, where for each $i = 1, 2, \dots, m - 1$ and each even $k = 0, 1, \dots, 2n - 2$, an edge (called a _brick edge_) is drawn to join $(i, k)$ to $(i + 1, k)$, whereas, for each even $i = 1, 2, \dots, m - 1$ and each odd $k = 1, 2, \dots, 2n - 1$, an edge (also called a _brick edge_) is drawn to join $(i, k)$ to $(i + 1, k)$. Finally, for each odd $k = 1, 2, \dots, 2n - 1$, an edge (called a _hooking edge_) is drawn to join $(1, k)$ to $(m, k + r)$. An edge in $C(2n, m, r)$ which is neither a brick edge nor a hooking edge is called a _flat edge_.


See also [Rainbow connection in brick product graphs][2].

> [![Figs. 1-3: The brick products C(10,1,5), C(10,2,4), and C(10,3,5).][3]][3]


  [1]: https://doi.org/10.1016/0012-365X(94)00077-V "Alspach, Brian; Chen, C. C.; McAvaney, Kevin. Discrete Math. 151, No. 1-3, 19-38 (1996). zbMATH review at https://zbmath.org/0855.05078"
  [2]: https://doisrpska.nub.rs/index.php/IMVI/article/view/4325 "Rao, K. Srinivasa; Murali, R.; Rajendra, S. K. Bull. Int. Math. Virtual Inst. 8, No. 1, 55-66 (2018). zbMATH review at https://zbmath.org/1438.05103"
  [3]: https://i.sstatic.net/XCkci.png