\(3\)-Connected Simple Graphs with The Same Genus Distributions

Yunsheng Zhang 1, Yichao Chen2
1BUSINESS SCHOOL, HUNAN UNIVERSITY, 410082 CHANGSHA, CHINA
2COLLEGE OF MATHEMATICS AND ECONOMETRICS, HUNAN UNIVERSITY, 410082 CHanc- SHA, CHINA

Abstract

The paper construct infinite classes of non-isomorphic \(3\)-connected simple graphs with the same total genus polynomial, using overlap matrix, symmetry and Gustin representation. This answers a problem (Problem \(3\) of Page \(38\)) of L.A. McGeoch in his PHD thesis.
The result is helpful for firms to make marketing decisions by calculating the graphs of user demand relationships of different complex ecosystems of platform products and comparing genus polynomials.