On the Betti numbers and gracefulness of some planar graphs

2012/10/30 by Imbesi, Maurizio, La Barbiera, Monica
#05C78 #13D02 #13F20 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1210.8198

Abstract

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.

Related

• Algebraic and geometric aspects of bipartite planar graphs
• Non-vanishingness of Betti numbers of edge ideals
• Graded Betti numbers of path ideals of cycles and lines
• Certain Homological Invariants of Bipartite Kneser Graphs
• Non-vanishing of Betti numbers of edge ideals and complete bipartite subgraphs