Stahl's real-negative-root conjecture for specified graph families

For each graph family listed in Example, let its genus polynomial be the polynomial whose coefficients count embeddings by genus. Stahl's conjecture. The zeros of the genus polynomials of the graphs listed in Example are real and negative. Stahl had verified the assertion for the linear families associated with items (i), (ii), and (iv), leaving the remaining listed families as conjectural cases.