Euler-Genus Distributions of Cubic Caterpillar-Halin Graphs

In 2011, 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 the overlap matrix, we obtain a recurrence relation for the Euler-genus polynomials of cubic caterpillar-Halin graphs. Explicit formulas for the embed...

Full description

Saved in:
Bibliographic Details
Published inBulletin of the Malaysian Mathematical Sciences Society Vol. 44; no. 4; pp. 2631 - 2658
Main Authors Zhang, Jinlian, Peng, Xuhui, Chen, Qiyao
Format Journal Article
LanguageEnglish
Published Singapore Springer Singapore 01.07.2021
Springer Nature B.V
Subjects
Algorithms
Applications of Mathematics
Caterpillars
Graphs
Mathematics
Mathematics and Statistics
Polynomials
05C10
Euler-genus polynomial
05C30
Overlap matrix
Embedding distribution
05A15
Cubic Halin graph
Online AccessGet full text

Cover

More Information
Summary:In 2011, 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 the overlap matrix, we obtain a recurrence relation for the Euler-genus polynomials of cubic caterpillar-Halin graphs. Explicit formulas for the embeddings of the cubic caterpillar-Halin graphs into surfaces with Euler-genus 0, 1 and 2 are also obtained.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-021-01084-0