Euler-genus distributions of cubic Halin graphs

Jinlian Zhang; Xuhui Peng

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Euler-genus distributions of cubic Halin graphs

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arxiv 1903.07060 v4 pith:RGVSJSDX submitted 2019-03-17 math.CO

Jinlian Zhang , Xuhui Peng This is my paper · ORCID

classification math.CO

keywords cubiceuler-genuscaterpillar-halingraphgraphshalinalgorithmcalculate

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abstract

Gross derived an $O(n^2)$-time algorithm to calculate the genus distribution of a given cubic Halin graph. In this paper, with the help of overlap matrix, we get a recurrence relation for the Euler-genus polynomial of cubic caterpillar-Halin graphs. Explicit formulas for the embeddings of cubic caterpillar-Halin graph into a surface with Euler-genus 0, 1 and 2 are also obtained.

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