A note on the values of independence polynomials at $-1$

Jonathan Cutler, Nathan Kahl

The independence polynomial $I(G;x)$ of a graph $G$ is $I(G;x)={\sum }_{k=1}^{\alpha (G)}{s}_k{x}^k$, where $s_k$ is the number of independent sets in $G$ of size $k$. The decycling number of…