Displaying similar documents to “A co-ideal based identity-summand graph of a commutative semiring”

On graph associated to co-ideals of commutative semirings

Yahya Talebi, Atefeh Darzi (2017)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let R be a commutative semiring with non-zero identity. In this paper, we introduce and study the graph Ω ( R ) whose vertices are all elements of R and two distinct vertices x and y are adjacent if and only if the product of the co-ideals generated by x and y is R . Also, we study the interplay between the graph-theoretic properties of this graph and some algebraic properties of semirings. Finally, we present some relationships between the zero-divisor graph Γ ( R ) and Ω ( R ) .

Some classes of perfect strongly annihilating-ideal graphs associated with commutative rings

Mitra Jalali, Abolfazl Tehranian, Reza Nikandish, Hamid Rasouli (2020)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let R be a commutative ring with identity and A ( R ) be the set of ideals with nonzero annihilator. The strongly annihilating-ideal graph of R is defined as the graph SAG ( R ) with the vertex set A ( R ) * = A ( R ) { 0 } and two distinct vertices I and J are adjacent if and only if I Ann ( J ) ( 0 ) and J Ann ( I ) ( 0 ) . In this paper, the perfectness of SAG ( R ) for some classes of rings R is investigated.

Regularity of powers of binomial edge ideals of complete multipartite graphs

Hong Wang, Zhongming Tang (2023)

Czechoslovak Mathematical Journal

Similarity:

Let G = K n 1 , n 2 , ... , n r be a complete multipartite graph on [ n ] with n > r > 1 and J G being its binomial edge ideal. It is proved that the Castelnuovo-Mumford regularity reg ( J G t ) is 2 t + 1 for any positive integer t .

Degree sums of adjacent vertices for traceability of claw-free graphs

Tao Tian, Liming Xiong, Zhi-Hong Chen, Shipeng Wang (2022)

Czechoslovak Mathematical Journal

Similarity:

The line graph of a graph G , denoted by L ( G ) , has E ( G ) as its vertex set, where two vertices in L ( G ) are adjacent if and only if the corresponding edges in G have a vertex in common. For a graph H , define σ ¯ 2 ( H ) = min { d ( u ) + d ( v ) : u v E ( H ) } . Let H be a 2-connected claw-free simple graph of order n with δ ( H ) 3 . We show that, if σ ¯ 2 ( H ) 1 7 ( 2 n - 5 ) and n is sufficiently large, then either H is traceable or the Ryjáček’s closure cl ( H ) = L ( G ) , where G is an essentially 2 -edge-connected triangle-free graph that can be contracted to one of the two graphs of order 10...

Semi n -ideals of commutative rings

Ece Yetkin Çelikel, Hani A. Khashan (2022)

Czechoslovak Mathematical Journal

Similarity:

Let R be a commutative ring with identity. A proper ideal I is said to be an n -ideal of R if for a , b R , a b I and a 0 imply b I . We give a new generalization of the concept of n -ideals by defining a proper ideal I of R to be a semi n -ideal if whenever a R is such that a 2 I , then a 0 or a I . We give some examples of semi n -ideal and investigate semi n -ideals under various contexts of constructions such as direct products, homomorphic images and localizations. We present various characterizations of this new...

Some results on the co-intersection graph of submodules of a module

Lotf Ali Mahdavi, Yahya Talebi (2018)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let R be a ring with identity and M be a unitary left R -module. The co-intersection graph of proper submodules of M , denoted by Ω ( M ) , is an undirected simple graph whose vertex set V ( Ω ) is a set of all nontrivial submodules of M and two distinct vertices N and K are adjacent if and only if N + K M . We study the connectivity, the core and the clique number of Ω ( M ) . Also, we provide some conditions on the module M , under which the clique number of Ω ( M ) is infinite and Ω ( M ) is a planar graph. Moreover, we give...

The Turán number of the graph 3 P 4

Halina Bielak, Sebastian Kieliszek (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

Let e x ( n , G ) denote the maximum number of edges in a graph on n vertices which does not contain G as a subgraph. Let P i denote a path consisting of i vertices and let m P i denote m disjoint copies of P i . In this paper we count e x ( n , 3 P 4 ) .

A note on the multiplier ideals of monomial ideals

Cheng Gong, Zhongming Tang (2015)

Czechoslovak Mathematical Journal

Similarity:

Let 𝔞 [ x 1 , ... , x n ] be a monomial ideal and 𝒥 ( 𝔞 c ) the multiplier ideal of 𝔞 with coefficient c . Then 𝒥 ( 𝔞 c ) is also a monomial ideal of [ x 1 , ... , x n ] , and the equality 𝒥 ( 𝔞 c ) = 𝔞 implies that 0 < c < n + 1 . We mainly discuss the problem when 𝒥 ( 𝔞 ) = 𝔞 or 𝒥 ( 𝔞 n + 1 - ε ) = 𝔞 for all 0 < ε < 1 . It is proved that if 𝒥 ( 𝔞 ) = 𝔞 then 𝔞 is principal, and if 𝒥 ( 𝔞 n + 1 - ε ) = 𝔞 holds for all 0 < ε < 1 then 𝔞 = ( x 1 , ... , x n ) . One global result is also obtained. Let 𝔞 ˜ be the ideal sheaf on n - 1 associated with 𝔞 . Then it is proved that the equality 𝒥 ( 𝔞 ˜ ) = 𝔞 ˜ implies that 𝔞 ˜ is principal.

The strong persistence property and symbolic strong persistence property

Mehrdad Nasernejad, Kazem Khashyarmanesh, Leslie G. Roberts, Jonathan Toledo (2022)

Czechoslovak Mathematical Journal

Similarity:

Let I be an ideal in a commutative Noetherian ring R . Then the ideal I has the strong persistence property if and only if ( I k + 1 : R I ) = I k for all k , and I has the symbolic strong persistence property if and only if ( I ( k + 1 ) : R I ( 1 ) ) = I ( k ) for all k , where I ( k ) denotes the k th symbolic power of I . We study the strong persistence property for some classes of monomial ideals. In particular, we present a family of primary monomial ideals failing the strong persistence property. Finally, we show that every square-free monomial...

Turán number of two vertex-disjoint copies of cliques

Caiyun Hu (2024)

Czechoslovak Mathematical Journal

Similarity:

The Turán number of a given graph H , denoted by ex ( n , H ) , is the maximum number of edges in an H -free graph on n vertices. Applying a well-known result of Hajnal and Szemerédi, we determine the Turán number ex ( n , K p K q ) of a vertex-disjoint union of cliques K p and K q for all values of n .

Saturation numbers for linear forests P 6 + t P 2

Jingru Yan (2023)

Czechoslovak Mathematical Journal

Similarity:

A graph G is H -saturated if it contains no H as a subgraph, but does contain H after the addition of any edge in the complement of G . The saturation number, sat ( n , H ) , is the minimum number of edges of a graph in the set of all H -saturated graphs of order n . We determine the saturation number sat ( n , P 6 + t P 2 ) for n 10 3 t + 10 and characterize the extremal graphs for n > 10 3 t + 20 .

Classification of rings with toroidal Jacobson graph

Krishnan Selvakumar, Manoharan Subajini (2016)

Czechoslovak Mathematical Journal

Similarity:

Let R be a commutative ring with nonzero identity and J ( R ) the Jacobson radical of R . The Jacobson graph of R , denoted by 𝔍 R , is defined as the graph with vertex set R J ( R ) such that two distinct vertices x and y are adjacent if and only if 1 - x y is not a unit of R . The genus of a simple graph G is the smallest nonnegative integer n such that G can be embedded into an orientable surface S n . In this paper, we investigate the genus number of the compact Riemann surface in which 𝔍 R can be embedded and...