The matching book embedding under some graph operations

Shao, Zeling (Hebei University of Technology)
Yao, Min (Hebei University of Technology)
Li, Zhiguo (Hebei University of Technology)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 14, No 1 (2026): Electronic Journal of Graph Theory and Applications

The matching book embedding of a graph G is an embedding of G with the vertices on the spine, and 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 embedding of G, denoted by mbt(G). In this paper, the exact matching book thickness of the corona product between a dispersible or nearly dispersible graph and a simple graph is determined. Additionally, the dispersibility of the edge product of a cycle and a simple graph is obtained. Finally the matching book thickness of the comb product of two dispersible graphs is obtained.