Results 11 to 20 of about 213,086 (270)
Stanley Depth of the Edge Ideal of Extended Gear Networks and Application in Circuit Analysis
Journal of Mathematics, 2022 Graph theory is widely used in power network analysis, complex network, and engineering calculation. Stanley depth is a geometric invariant of the module which is closely related to an algebraic invariant called depth of the module.
Guiling Zeng +4 more
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The regularity of binomial edge ideals of graphs [PDF]
AUT Journal of Mathematics and Computing, 2020 In this paper, we study the Castelnuovo-Mumford regularity and the graded Betti numbers of the binomial edge ideals of some classes of graphs. Our special attention is devoted to a conjecture which asserts that the number of maximal cliques of a graph ...
Sara Saeedi Madani, Dariush Kiani
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EDGE IDEALS OF WEIGHTED GRAPHS [PDF]
Journal of Algebra and Its Applications, 2013 We study weighted graphs and their "edge ideals" which are ideals in polynomial rings that are defined in terms of the graphs. We provide combinatorial descriptions of m-irreducible decompositions for the edge ideal of a weighted graph in terms of the combinatorics of "weighted vertex covers". We use these, for instance, to say when these ideals are m-
Paulsen, Chelsey, Sather-Wagstaff, Sean
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Induced Matchings and the v-Number of Graded Ideals
Mathematics, 2021 We give a formula for the v-number of a graded ideal that can be used to compute this number. Then, we show that for the edge ideal I(G) of a graph G, the induced matching number of G is an upper bound for the v-number of I(G) when G is very well-covered,
Gonzalo Grisalde +2 more
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Journal of Algebraic Combinatorics, 2012 The paper under review is inspired by the question of for which graphs do all powers of the edge ideals have linear resolutions. It is known (cf. \textit{D. Eisenbud} et al., [Compos. Math. 141, No. 6, 1460--1478 (2005; Zbl 1086.14044)] and \textit{H.T. Hà} and \textit{A. Van Tuyl} [J. Algebra 309, No. 1, 405--425 (2007; Zbl 1151.13017)]) that the edge
Nevo, Eran, Peeva, Irena
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Generalization of f-Graphs and Their Algebraic Aspects
Journal of Mathematics, 2023 The notion of f-graphs and f-ideals are relatively new and have been studied in many papers. In this paper, we have generalized the idea of f-graphs and f-ideals to quasi f-graphs and quasi f-ideals, respectively. We have characterized all quasi f-graphs
Fazal Ur Rehman +3 more
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Monomial s-sequences arising from graph ideals
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2023 Ideals arising from graphs are investigated via s-sequence theory. In particular, the notion of s-sequence for the generators of the edge ideal I(G) of an acyclic graph G is considered for describing the Groebner basis of the relation ideal J of the ...
Maurizio Imbesi, Monica La Barbiera
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Sequentially Cohen-Macaulay edge ideals [PDF]
Proceedings of the American Mathematical Society, 2007 Let G be a simple undirected graph on n vertices, and let I(G) \subseteq R = k[x_1,...,x_n] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear.
Francisco, Christopher A. +1 more
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Binomial Edge Ideals of Graphs [PDF]
The Electronic Journal of Combinatorics, 2012 We characterize all graphs whose binomial edge ideals have a linear resolution. Indeed, we show that complete graphs are the only graphs with this property. We also compute some graded components of the first Betti number of the binomial edge ideal of a graph with respect to the graphical terms.
Kiani, Dariush, Saeedi, Sara
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Exploring the Relationships Between Four Aging Ideals: A Bibliometric Study
Frontiers in Public Health, 2022 When examining research articles on the aging strategies, four ideals (i.e., successful aging, healthy aging, productive aging and active aging) could be explored by conducting bibliometric analyses.
Ka Lin +5 more
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