A class of cubic graphs is introduced for which the genus is a nonadditive function of the genus of subgraphs. This provides a small (28 node) counterexample to Duke’s conjecture concerning the relation of the Betti number to the genus of a graph.
KeywordsPlanar Graph Additive Function Previous Lemma Betti Number Free Edge
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- 2.R.A. Duke,The genus, regional number, and the Betti number of a graph, Canad. J. Math.18, 817–822.Google Scholar