On Gorenstein Circulant Graphs and Gorenstein SQC 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 $C_n(1,\dots ,d)$ for some $d\le n/2$, then $G$ is Gorenstein if and only if $G\cong t{K}_2$, $G\cong t\overline{C_n}$ or $G\cong t{C}_{13}(1,5)$ for some integers $t$ and $n\ge 4$. Also we prove that if $G$ is a \mathcal{SQC}\ graph, then $G$ is Gorenstein if and only if each component of $G$ is either an edge or a 5-cycle.

References in corpus (6)

• Chordality of Clutters with Vertex Decomposable Dual and Ascent of Clutters
• Some algebraic invariants of edge ideal of circulant graphs
• The regularity of some families of circulant graphs
• Trung's Construction and the Charney-Davis Conjecture
• 2-dimensional vertex decomposable circulant graphs
• Some Combinatorial Characterizations of Gorenstein Graphs with Independence Number Less than Four

Cited by in corpus (1)

• Well-covered Unitary Cayley Graphs of Matrix Rings over Finite Fields and Applications