Abstract
Elimination ideals are regarded as a special type of Borel type ideals, obtained from degree sequence of a graph, introduced by Anwar and Khalid. In this paper, we compute graphical degree stabilities of K n ∨ C m and K n ∗ C m by using the DVE method. We further compute sharp upper bound for Castelnuovo–Mumford regularity of elimination ideals associated to these families of graphs.
Highlights
Let S k[x1, . . . , xn], n ≥ 2 be a polynomial ring in n variables over an infinite field k
Bayer and Stillman noted that a monomial ideal I ⊂ S is of Borel type, if it satisfies the following condition:
E regularity of an ideal I is defined as reg(I) max j: βi,i+j(I) ≠ 0, where βij’s are the graded Betti numbers of ideal I. e regularity of monomial ideals of Borel type was extensively studied
Summary
Let S k[x1, . . . , xn], n ≥ 2 be a polynomial ring in n variables over an infinite field k. We compute the graphical degree stabilities of join and corona product of above graphs by using the dominating vertex elimination method (see Lemmas 1 and 2). Let H be a simple finite and connected graph; the length of the maximum chain of induced, non-scattered, subgraphs of H obtained by successively applying DVE method is called graphical degree words, stability and if H H0H1···Hr is is denoted as Stabd(H).
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