On Gorenstein circulant graphs

Abstract

We characterize some graphs with a Gorenstein edge ideal. In particular, we show that if G is a circulant graph with vertex degree at most four or a circulant graph of the form Cn(1,…,d) for some d≤n/2, then G is Gorenstein if and only if G≅tK2 or G≅tCn‾ or G≅tC13(1,5) for some integers t and n≥4.