On the classification and dispersability of circulant graphs with two jump lengths

In this paper, we give the classification of circulant graphs $C(\mathbb{Z}_{n},S)$ with $|S|=2$ and completely solve the dispersability of circulant graphs $C(\mathbb{Z}_{n},\{1, k\})$

Matching Book Thickness of Halin Graphs

The \emph{matching book embedding} of a graph $G$ is to arrange its vertices on the spine, and draw its edges into the pages so that the edges on every page do not intersect each other and the maximum degree of vertices on every page is one. The \emph{matching book thickness} is the minimum number of pages in which the graph $G$ can be matching embedded. In this paper, the matching book thickness of Halin graphs is determined