Some Applications of Wagner's Weighted Subgraph Counting Polynomial

We use Wagner's weighted subgraph counting polynomial to prove that the partition function of anti-ferromagnetic Ising model on line graphs is real rooted and roots edge cover have absolute value at most $4$. more generally show a $k$-uniform hypergraph $2^k$, discuss applications this domination polynomials graphs. moreover how our results relate efficient algorithms for approximately computing evaluations these polynomials.