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Journal of Combinatorial Mathematics and Combinatorial Computing

  • Research article

The Genus of Edge Amalgamations of a Type of Graph

Zeling Shao1, Yanpei Liu2, Zhiguo Li1
1Department of Mathematics, Hebei University of Technology, Tianjin 300401, China
2Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China
  • Published: 28/02/2014

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 \( 1 \).

Keywords: genus, joint tree, edge amalgamation, orientable surface, embedding
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Citation
Zeling Shao, Yanpei Liu, Zhiguo Li. The Genus of Edge Amalgamations of a Type of Graph[J], Journal of Combinatorial Mathematics and Combinatorial Computing, Volume 088. 161-167. DOI: .