The dispersability of the Kronecker cover of the product of complete graphs and cycles

Shao, Zeling (Department of Mathematics, Hebei University of Technology, China)
Cui, Yaqin (Department of Mathematics, Hebei University of Technology, China)
Li, Zhiguo (Department of Mathematics, Hebei University of Technology, China)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 12, No 1 (2024): Electronic Journal of Graph Theory and Applications

The Kronecker cover of a graph G is the Kronecker product of G and K2. The matching book embedding of a graph G is an embedding of G with the vertices on the spine, each edge within a single page so that the edges on each page do not intersect and the degree of vertices on each page is at most one. The matching book thickness of G is the minimum number of pages in a matching book embeddding of G and it denoted by mbt(G). A graph G is dispersable if mbt(G)=Δ(G), nearly dispersable if mbt(G)=Δ(G)+1. In this paper, the dispersability of the Kronecker cover of the Cartesian product of complete graphs Kp and cycles Cq is determined.