Journal of the Ramanujan Mathematical Society

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On Generalized Graph Ideals of Complete Bipartite Graphs


Affiliations
1 University of Messina, Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, Viale F. Stagno d’Alcontres 31, I-98166 Messina, Italy
2 University of Catania, Department of Industrial Engineering, Viale A. Doria 6, Building 3, I-95125 Catania, Italy
3 University of Palermo, Department of Civil, Environmental, Aerospace, Material Engineering, Viale delle Scienze, Building 8, I-90128 Palermo, Italy
     

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Let S = K[X1, . . . , Xn; Y1, . . . , Ym] be the polynomial ring in two sets of variables over a field K. Using the notion of linear quotients, we investigate significative classes of graph ideals of S that have a linear resolution, namely the generalized graph ideals, in order to compute standard algebraic invariants of S modulo such ideals. Moreover we are able to determine the structure of the ideals of vertex covers for such generalized graph ideals.
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  • On Generalized Graph Ideals of Complete Bipartite Graphs

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Authors

Maurizio Imbesi
University of Messina, Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, Viale F. Stagno d’Alcontres 31, I-98166 Messina, Italy
Monica La Barbiera
University of Catania, Department of Industrial Engineering, Viale A. Doria 6, Building 3, I-95125 Catania, Italy
Paola Lea Stagliano
University of Palermo, Department of Civil, Environmental, Aerospace, Material Engineering, Viale delle Scienze, Building 8, I-90128 Palermo, Italy

Abstract


Let S = K[X1, . . . , Xn; Y1, . . . , Ym] be the polynomial ring in two sets of variables over a field K. Using the notion of linear quotients, we investigate significative classes of graph ideals of S that have a linear resolution, namely the generalized graph ideals, in order to compute standard algebraic invariants of S modulo such ideals. Moreover we are able to determine the structure of the ideals of vertex covers for such generalized graph ideals.