Abstract
In [2], Chen et al. showed that the average genus for a graph of maximum degree at most 3 is at least 1/2 its maximum genus. In this paper, the structure for a graph of maximum degree at most 3 with average genus equal to 1/2 its maximum genus is described. Furthermore, LetH be a subgraph ofG and γavg(G) = γavg(H). It’s shown thatG can be obtained by a series operations of type I and II onH.
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