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.
Citation
J. Luviano. E. Reyes. "On vertex decomposable and Cohen-Macaulay regular graphs." Rocky Mountain J. Math. 48 (8) 2625 - 2651, 2018. https://doi.org/10.1216/RMJ-2018-48-8-2625
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