In this article, we obtain an upper bound for the regularity of binomial edge ideal a graph whose every block is either cycle or clique. As consequence, cactus graph. We also identify certain subclass attaining bound.

Let [Formula: see text] be a weighted oriented graph and its edge ideal. We provide one method to find all the minimal generators of text], where is maximal strong vertex cover intersections irreducible ideals associated covers contained in text]. If an induced digraph under certain condition on we show that for some implies necessary sufficient equality ordinary symbolic powers ideal union two...

We prove two recent conjectures on some upper bounds for the Castelnuovo-Mumford regularity of the binomial edge ideals of some different classes of graphs. We prove the conjecture of Matsuda and Murai for chordal graphs. We also prove the conjecture due to the authors for a class of chordal graphs. We determine the regularity of the binomial edge ideal of the join of graphs in terms of the reg...

this paper consider the   general  forms of $(alpha,beta)$-fuzzyleft ideals (right ideals, bi-ideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. special attention is paid to$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interiorideals) and some related  pr...

We determine the arithmetical rank of every edge ideal of a Ferrers graph.

Let C be a clutter and let I be its edge ideal. We present a combinatorial description of the minimal generators of the symbolic Rees algebra Rs(I) of I . It is shown that the minimal generators of Rs(I) are in one to one correspondence with the irreducible parallelizations of C. From our description some major results on symbolic Rees algebras of perfect graphs and clutters will follow. As a b...

Let G be a finite graph on the vertex set [d] = {1, . . . , d} with the edges e1, . . . , en and K[t] = K[t1, . . . , td] the polynomial ring in d variables over a field K. The edge ring of G is the semigroup ringK[G] which is generated by those monomials t = titj such that e = {i, j} is an edge of G. Let K[x] = K[x1, . . . , xn] be the polynomial ring in n variables over K and define the surje...