Graph-counting polynomials for oriented graphs

Abstract

If $\mathcal{F}$ is a set of subgraphs $F$ of a finite graph $E$ we define a graph-counting polynomial $$p_{\mathcal{F}}(z)=\sum _{F\in \mathcal{F}}{z}^{|F|}$$ In the present note we consider oriented graphs and discuss some cases where $\mathcal{F}$ consists of unbranched subgraphs $E$. We find several situations where something can be said about the location of the zeros of $p_{\mathcal{F}}$.

6 pages

References in corpus (2)

• Location of the Lee-Yang zeros and absence of phase transitions in some Ising spin systems
• Phase transitions with four-spin interactions