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Winter 2020 $b$-vectors of chordal graphs
Luis Pedro Montejano, Luis Núñez-Betancourt
J. Commut. Algebra 12(4): 539-557 (Winter 2020). DOI: 10.1216/jca.2020.12.539

Abstract

The b-vector (b1,b2,bd) of a graph G is defined in terms of its clique vector (c1,c2,cd) by the equation i=1dbi(x+1)i1=i=1dcixi1, where d is the largest cardinality of a clique in G. We study the relation of the b-vector of a chordal graph G with some structural properties of G. In particular, we show that the b-vector encodes different aspects of the connectivity and clique dominance of G. Furthermore, we relate the b-vector with the Betti numbers of the Stanley–Reisner ring associated to clique simplicial complex of G.

Citation

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Luis Pedro Montejano. Luis Núñez-Betancourt. "$b$-vectors of chordal graphs." J. Commut. Algebra 12 (4) 539 - 557, Winter 2020. https://doi.org/10.1216/jca.2020.12.539

Information

Received: 23 September 2019; Revised: 9 October 2019; Accepted: 17 October 2019; Published: Winter 2020
First available in Project Euclid: 5 January 2021

MathSciNet: MR4194940
Digital Object Identifier: 10.1216/jca.2020.12.539

Subjects:
Primary: 05C25, 05E40, 13D02, 13F55

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.12 • No. 4 • Winter 2020
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