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Main Authors:	Imbesi, Maurizio, La Barbiera, Monica
Format:	Preprint
Published:	2012
Subjects:	Commutative Algebra 05C78, 13D02, 13F20
Online Access:	https://arxiv.org/abs/1210.8198
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author	Imbesi, Maurizio La Barbiera, Monica
author_facet	Imbesi, Maurizio La Barbiera, Monica
contents	In this article bipartite planar graphs St_r are investigated, r the number of their plane regions. Bounds for the graded Betti numbers and the projective dimension of the quotient ring associated to such graphs are discussed. We prove that r is related to algebraic invariants that arise from the projective resolution of the edge ideal of the graph. We also deal with labeling methods for certain graphs and show that graphs St_r admit a graceful numbering of their edges.
format	Preprint
id	arxiv_https___arxiv_org_abs_1210_8198
institution	arXiv
publishDate	2012
record_format	arxiv
spellingShingle	On the Betti numbers and gracefulness of some planar graphs Imbesi, Maurizio La Barbiera, Monica Commutative Algebra 05C78, 13D02, 13F20 In this article bipartite planar graphs St_r are investigated, r the number of their plane regions. Bounds for the graded Betti numbers and the projective dimension of the quotient ring associated to such graphs are discussed. We prove that r is related to algebraic invariants that arise from the projective resolution of the edge ideal of the graph. We also deal with labeling methods for certain graphs and show that graphs St_r admit a graceful numbering of their edges.
title	On the Betti numbers and gracefulness of some planar graphs
topic	Commutative Algebra 05C78, 13D02, 13F20
url	https://arxiv.org/abs/1210.8198

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