The Genus of Edge Amalgamations of a Type of Graph

Abstract

If \( G_1 \) and \( G_2 \) are two graphs, then the edge amalgamation \( G_1 *_e G_2 \) 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 \( \gamma(G_1 *_e G_2 *_e \ldots *_e G_n) = \lceil \frac{n}{2} \rceil \) where \( G_i \) (\( 1 \leq i \leq n \)) is a critical graph of minimum genus \( 1 \).