Some Combinatorial Characterizations of Gorenstein Graphs with Independence Number Less than Four

Mohammad Reza Oboudi, Ashkan Nikseresht

Let $\alpha =\alpha (G)$ be the independence number of a simple graph $G$ with $n$ vertices and $I(G)$ be its edge ideal in $S=K[x_1,\dots ,x_n]$. If $S/I(G)$ is Gorenstein, the graph $G$ is…