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math.CO2025
Matrix Quasi-tree Theorem
Qingying Deng, Xian'an Jin, Qi Yan +1
Building on prior work that established Matrix Quasi-tree Theorems for special embedded graphs, in this paper, we develop a comprehensive theory applicable to all embedded graphs.…
math.CO2025
Proof of a conjecture of Fomichev and Karev
Qi Yan, Qingying Deng, Xian'an Jin
We prove a conjecture of Fomichev and Karev [{European J. Combin.} 127 (2025) 104160] by showing the equality of two graph invariants: , defined via graph colorings, and , de…
math.CO2025
Introducing a vertex polynomial invariant for embedded graphs
Qi Yan, Qingying Deng, Metrose Metsidik
The ribbon group action extends geometric duality and Petrie duality by defining two embedded graphs as twisted duals precisely when they lie within the same orbit under this group…