Rocky Mountain Journal of Mathematics

On vertex decomposable and Cohen-Macaulay regular graphs

J. Luviano and E. Reyes

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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

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1546138824

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

Zentralblatt MATH identifier
1402.05177

Subjects
Primary: 05C75: Structural characterization of families of graphs 05E45: Combinatorial aspects of simplicial complexes 13F55: Stanley-Reisner face rings; simplicial complexes [See also 55U10]

Keywords
Pure vertex decomposability Cohen Macaulay regular graphs generalized Petersen graphs transitive graphs and well-covered

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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