The genus polynomials of cross-ladder digraphs in orientable surfaces
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摘要:
Some results about the genus distributions of graphs are known, but little is known about those of digraphs. In this paper, the method of joint trees initiated by Liu is generalized to compute the embedding genus distributions of digraphs in orientable surfaces. The genus polynomials for a new kind of 4-regular digraphs called the cross-ladders in orientable surfaces are obtained. These results are close to solving the third problem given by Bonnington et al.