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- W1825428645 abstract "Our concern is deriving genus distributions of graphs ob- tained by surgical operations on graphs whose genus distribution is known. One operation in focus here is adding an edge. The other is splitting a vertex, for which the inverse operation is edge-contraction. Our main result is this Splitting Theorem: Let G be a graph and w a 4-valent vertex of G. Let H1, H2, and H3 be the three graphs into which G can be split at w, so that the two new vertices of each split are 3-valent. Then 2gd(G) = gd(H1) + gd(H2) + gd(H3)." @default.
- W1825428645 created "2016-06-24" @default.
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- W1825428645 date "2010-01-01" @default.
- W1825428645 modified "2023-09-26" @default.
- W1825428645 title "Genus distribution of graphs under surgery: adding edges and splitting vertices" @default.
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