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Partial-dual Euler-genus polynomials for two classes of bouquets
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维普
[European J.Combin.,2020,86:Paper No.103084,20 pp.]introduced the concept of partial-dual Euler-genus polynomial in the ribbon graphs and gave the interpolation conjecture.That is,the partial-dual Euler-genus polynomial for any non-orientable ribbon graph is interpolating.In fact,[European J.Combin.,2022,102:Paper No.103493,7 pp.]gave two classes of counterexamples to deny the conjecture,and only one or two of the side loops contained in the two classes of bouquets were non-orientable.On the basis of[European J.Combin.,2022,102:Paper No.103493,7 pp.],we further calculate the partial-dual Euler-genus polynomials of two other classes of bouquets.One is non-inter-polating,whose side loop has an arbitrary number of non-orientable loops.The other is interpolating,whose side loop has an arbitrary number of both non-orientable loops and orientable loops.
万方数据
维普
