Unimodality of Independence Polynomials of Very Well-Covered Graphs

Abstract

In this paper, we show that the independence polynomial \(I(G^*; x)\) of \(G^*\) is unimodal for any graph \(G^*\) whose skeleton \(G\) has stability number \(\alpha(G) \leq 8\). In addition, we show that the independence polynomial of \(K^*_{2,n}\) is log-concave with a unique mode.