The Genus of Edge Amalgamations of a Type of Graph

Abstract

If $G_1$ and $G_2$ are two graphs, then the edge amalgamation $G_1{\ast }_e{G}_2$ is defined to be the graph obtained by identifying some given edge of $G_1$ with some given edge of $G_2$. In this paper, it is shown that $\gamma (G_1{\ast }_e{G}_2{\ast }_e\dots {\ast }_e{G}_n)=\lceil \frac{n}{2}\rceil$ where $G_i$ ($1\le i\le n$) is a critical graph of minimum genus $1$.