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 of the graph arising from the projective resolution of the edge ideal. We also deal with labeling methods for some graphs and show that graphs St_r admit a graceful numbering of their edges.
On the Betti numbers and gracefulness of some planar graphs
Imbesi M.;La Barbiera M.
In corso di stampa
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 of the graph arising from the projective resolution of the edge ideal. We also deal with labeling methods for some graphs and show that graphs St_r admit a graceful numbering of their edges.File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
