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Monica La Barbiera

Publications and source records attributed to Monica La Barbiera.

10 recordsLinked to original sources
arXiv2024

On the Betti numbers and gracefulness of some planar graphs

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.

math.AC↗
arXiv2024

Algebraic and geometric aspects of bipartite planar graphs

Let B_{2t} be a bipartite planar graph with an even number of regions. We are able to find bounds for the graded Betti numbers and the projective dimension of the quotient ring associated to the graph. We also will investigate the minimal vertex covers and the maximum matchings related to such a graph.

math.AC↗
arXiv2024

Algorithmic releases on the spanning trees of suitable graphs

In this paper algebraic and combinatorial properties and a computation of the number of the spanning trees are developed for certain graphs. To this purpose, an original method, independent of the spectrum of the Laplacian matrix associated to the graph, is discussed. It represents an alternative process to compute how many and which are the spanning trees of any graph and substantially consists in joining the spanning trees on the ground of the number of common edges between the inner cycles of it. The algorithm and its source code for determining the collection of all edge-sets of the spanning trees for the class of Jahangir graphs are displayed. An application involving such graphs in order to get a satisfactory degree of security in transmitting confidential information is given, and finally symmetry properties of them are highlighted.

math.CO↗
arXiv2024

Generalized mixed product ideals whose powers have a linear resolution

In this paper we study classes of monomial ideals for which all of its powers have a linear resolution. Let K[x_{1},x_{2}] be the polynomial ring in two variables over the field K, and let L be the generalized mixed product ideal induced by a monomial ideal I. It is shown that, if I\subset K[x_1,x_2] and the ideals substituting the monomials in I are Veronese type ideals, then L^{k} has a linear resolution for all k\geq 1. Furthermore, we compute some algebraic invariants of generalized mixed product ideals induced by a transversal polymatroidal ideal.

math.AC↗
arXiv2024

Unmixedness of generalized Veronese bi-type ideals

In this paper, some algebraic invariants of generalized Veronese bi-type ideals are computed. We characterize the unmixed generalized Veronese bi-type ideals and we give a description of their associated prime ideals.

math.AC↗
arXiv2024

Combinatorics of the integral closure of edge ideals of strong quasi-n-partite graphs

Combinatorial properties of some ideals related to strong quasi-n-partites graphs are examined. We prove that the edge ideal of a strong quasi-n-partite graph is not integrally closed and we give an expression for its integral closure. Moreover, we are able to determine the structure of the ideals of vertex covers for the edge ideals associated to a strong quasi-n-partite graph.

math.AC↗
arXiv2024

Combinatorial properties of strong quasi-n-partite graphs

Monomial ideals corresponding to strong quasi-n-partite graphs are considered. Some algebraic and combinatorial properties of generalized graph ideals of a strong quasi-n-partite graph are studied. Furthermore, we show that the edge ideal of a strong quasi-n-partite graph is Cohen-Macaulay.

math.AC↗
arXiv2014

Algebraic properties of universal squarefree lexsegment ideals

Let K be a field and let A be the polynomial ring in n variables with coefficients in the field K We study the universal squarefree lexsegment ideals in A. We put our attention on their combinatorics computing some invariants. Moreover we study the link between such special class of squarefree lexsegment ideals and the so called s-sequences.

math.AC↗
arXiv2012

Monomial ideals of graphs with loops

We investigate, using the notion of linear quotients, significative classes of connected graphs whose monomial edge ideals, not necessarily squarefree, have linear resolution, in order to compute standard algebraic invariants of the polynomial ring related to these graphs modulo such ideals. Moreover we are able to determine the structure of the ideals of vertex covers for the edge ideals associated to the previous classes of graphs which can have loops on any vertex. Lastly, it is showed that these ideals are of linear type.

math.RA↗