Limit for the Euler-genus distributions of ladder-like sequences of graphs

In this paper, we demonstrate a method for calculating the production matrices for the Euler-genus polynomials of H -linear families of graphs. Particularly, for any ladder-like sequence of graphs, we give its explicit production matrix that leads to a recurrence relation. Based on this recurrence r...

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Bibliographic Details
Published inJournal of algebraic combinatorics Vol. 54; no. 2; pp. 559 - 574
Main Authors Zhang, Jinlian, Peng, Xuhui, Zhang, Xianglin
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2021
Springer Nature B.V
Subjects
Combinatorics
Computer Science
Convex and Discrete Geometry
Graphs
Group Theory and Generalizations
Lattices
Mathematical analysis
Mathematics
Mathematics and Statistics
Normal distribution
Order
Ordered Algebraic Structures
Polynomials
Ladder-like sequence of graphs
Normal distribution
05C30
Primary:05C10
Limit
Secondary:05A15
Euler-genus distribution
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Summary:In this paper, we demonstrate a method for calculating the production matrices for the Euler-genus polynomials of H -linear families of graphs. Particularly, for any ladder-like sequence of graphs, we give its explicit production matrix that leads to a recurrence relation. Based on this recurrence relation, we show that the Euler-genus distributions of any ladder-like sequence of graphs are asymptotic to a normal distribution. Since the genus polynomials of the ladder-like sequence of graphs have already been calculated by Chen et al.(J Algebr Combin 52:137–155, 2020), their crosscap-number polynomials are also known.
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-021-01014-0