## Rocky Mountain Journal of Mathematics

### On vertex decomposable and Cohen-Macaulay regular graphs

#### Abstract

We characterize the Cohen-Macaulay property for generalized Petersen graphs and $3$-regular graphs. In particular, we prove that these graphs are vertex decomposable. Also, we characterize pure vertex decomposability for $4$-transitive graphs without $5$-holes. Finally, we study the small cycles of well-covered and Cohen-Macaulay regular graphs.

#### Article information

Source
Rocky Mountain J. Math., Volume 48, Number 8 (2018), 2625-2651.

Dates
First available in Project Euclid: 30 December 2018

https://projecteuclid.org/euclid.rmjm/1546138824

Digital Object Identifier
doi:10.1216/RMJ-2018-48-8-2625

Zentralblatt MATH identifier
1402.05177

#### Citation

Luviano, J.; Reyes, E. On vertex decomposable and Cohen-Macaulay regular graphs. Rocky Mountain J. Math. 48 (2018), no. 8, 2625--2651. doi:10.1216/RMJ-2018-48-8-2625. https://projecteuclid.org/euclid.rmjm/1546138824

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