A face polynomial invariant for embedded graphs

Hongxia Ma; Metrose Metsidik

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arXiv · 2611.05090

A face polynomial invariant for embedded graphs

Hongxia Ma·Metrose Metsidik

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Abstract

We introduce the face polynomial of a ribbon graph, a generating function for face numbers under the ribbon group action. It addresses the face-count case of the Ellis--Monaghan--Moffatt question on twisted duality. We derive deletion--contraction recursions and prove that this polynomial coincides with the vertex polynomial for $\langleδ\rangle$, $\langleδτ\rangle$, and $\langleδ,τ\rangle$. We characterize monomial cases and obtain formulas and recursions for Euler-genus partial-twuality polynomials. For orientable graphs, we show that the partial-dual face polynomial has both parities whenever an edge exists, so the partial-dual Euler-genus polynomial has only even exponents.

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BibTeX RIS

Hongxia Ma, Metrose Metsidik. 2026-11-03. A face polynomial invariant for embedded graphs. https://arxiv.org/abs/2611.05090

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