Matching Book Embedding of the Cartesian Product of a Complete Graph and a Cycle

The $book$ $embedding$ of a graph $G$ is to place the vertices of $G$ on the spine and draw the edges to the pages so that the edges in the same page do not cross with each other. The book embedding is $matching$ if the pages have maximum degree $1$. The $matching$ $book$ $thickness$ is the minimum number of pages in which graphs can be matching book embedded. In this paper, we show that the matching book thickness of the Cartesian product $K_p\mathrm{\square }{C}_q$of a complete graph $K_p$ and a cycle $C_q$ is equal to $\mathrm{\Delta }(K_p\mathrm{\square }{C}_q)+1$.