A new vertex polynomial for ribbon graphs tracks vertex counts over ribbon group orbits, and for bouquets it depends only on the signed intersection graph.
Chmutov, Generalized duality for graphs on surfaces and the signed Bollob´ as- Riordan polynomial,J
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Introducing a vertex polynomial invariant for embedded graphs
A new vertex polynomial for ribbon graphs tracks vertex counts over ribbon group orbits, and for bouquets it depends only on the signed intersection graph.