In this paper, we investigate the class of planar k-partite graphs B_{2,t}, characterized by a specific recursive edge structure and partitioned into independent vertex sets. We compute the maximal independent sets and analyze key algebraic invariants of the associated edge ideals. In particular, we determine the vertex covering number, the induced matching number, the projective dimension, and the Castelnuovo-Mumford regularity of the quotient ring by powers of the edge ideal. We also discuss the unmixedness of these ideals and provide explicit formulas for all key invariants, highlighting the combinatorial-algebraic interplay in the study of planar graphs.
Maximal independent sets and combinatorial properties of the planar B_{2,t} k-partite graphs
MAURIZIO IMBESI;MONICA LA BARBIERA;
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Abstract
In this paper, we investigate the class of planar k-partite graphs B_{2,t}, characterized by a specific recursive edge structure and partitioned into independent vertex sets. We compute the maximal independent sets and analyze key algebraic invariants of the associated edge ideals. In particular, we determine the vertex covering number, the induced matching number, the projective dimension, and the Castelnuovo-Mumford regularity of the quotient ring by powers of the edge ideal. We also discuss the unmixedness of these ideals and provide explicit formulas for all key invariants, highlighting the combinatorial-algebraic interplay in the study of planar graphs.Pubblicazioni consigliate
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