Abstract
The vertex v of a graph G is called a 1-critical-vertex for the maximum genus of the graph, or for simplicity called 1-critical-vertex, if G-v is a connected graph and °M(G - v) = °M(G) - 1. In this paper, through the joint-tree model, we obtained some types of 1-critical-vertex, and get the upper embeddability of the Spiral Snm .
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