Cohen-Macaulayness of triangular graphs

Abstract

We study the Cohen-Macaulay property of triangular graphs $T_n$. We show that $T_2$, $T_3$ and $T_5$ are Cohen-Macaulay graphs, and that $T_4$, $T_6$, $T_8$ and $T_n$ are not Cohen-Macaulay graphs, for $n\ge 10$. Finally, we prove that over fields of characteristic zero $T_7$ and $T_9$ are Cohen-Macaulay.

10 pages, 2 figures

References in corpus (1)

• Regularity and Planarity of Token Graphs

Cited by in corpus (3)

• On the Connectivity of Token Graphs of Trees
• Independence numbers of some double vertex graphs and pair graphs
• The Edge-connectivity of Token Graphs