Genus Polynomials of Cubic Graphs with Non-Real Roots

MacKenzie Carr, Varpreet Dhaliwal, Bojan Mohar

Given a graph $G$, its genus polynomial is ${\Gamma }_G(x)={\sum }_{k\ge 0}{g}_k(G)x^k$, where $g_k(G)$ is the number of 2-cell embeddings of $G$ in an orientable surface of genus $k$. The…