scholarly journals The Tensor Product of Zero-Divisor Graphs of Variation Monogenic Semigroups

2021 ◽  
pp. 1-4
Author(s):  
Abolape Akwu ◽  
Bana Al Subaiei
Keyword(s):  
Tensor Product ◽  
Zero Divisor ◽  
Product Graphs ◽  
Domination Numbers

The tensor product of zero-divisor graphs of variation monogenic semigroups Γ(VS_Mn^1) and Γ(VS_Mm^2) is studied. The vertices(x_1^i,x_2^j) and (x_1^k,x_2^f) of the tensor product of this graph are adjacent whenever gcd(i,k)=1,i+k>n,gcd(j,f)=1 ,j+f>m. Some properties of tensor product graphs are obtained, such as girth, diameter, chromatic, clique and domination numbers.

Some Results on the Domination Number of a Zero-divisor Graph

2014 ◽  
Vol 57 (3) ◽  
pp. 573-578 ◽  
Author(s):  
Sima Kiani ◽  
Hamid Reza Maimani ◽  
Reza Nikandish
Keyword(s):  
Noetherian Ring ◽  
Zero Divisor ◽  
Domination Number ◽  
Total Domination ◽  
Ore Extension ◽  
Commutative Noetherian Ring ◽  
Zero Divisor Graph ◽  
Domination Numbers

AbstractIn this paper, we investigate the domination, total domination, and semi-total domination numbers of a zero-divisor graph of a commutative Noetherian ring. Also, some relations between the domination numbers of Γ(R/I) and Γ1(R), and the domination numbers of Γ(R) and Γ(R[x, α, δ]), where R[x, α, δ] is the Ore extension of R, are studied.

scholarly journals Vertex Degrees and Isomorphic Properties in Complement of an m-Polar Fuzzy Graph

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Ch. Ramprasad ◽  
P. L. N. Varma ◽  
S. Satyanarayana ◽  
N. Srinivasarao
Keyword(s):  
Graph Theory ◽  
Tensor Product ◽  
Computer Science ◽  
Computational Intelligence ◽  
Cartesian Product ◽  
Combinatorial Problems ◽  
Fuzzy Graph ◽  
Normal Product ◽  
Product Graphs ◽  
Vertex Degrees

Computational intelligence and computer science rely on graph theory to solve combinatorial problems. Normal product and tensor product of an m-polar fuzzy graph have been introduced in this article. Degrees of vertices in various product graphs, like Cartesian product, composition, tensor product, and normal product, have been computed. Complement and μ-complement of an m-polar fuzzy graph are defined and some properties are studied. An application of an m-polar fuzzy graph is also presented in this article.

On the fixed-point type Sylvester matrix equations over complete commutative dioids

2014 ◽  
Vol 27 ◽  
Author(s):  
Benham Hashemi ◽  
Mahtab Mirzaei Khalilabadi ◽  
Hanieh Tavakolipour
Keyword(s):  
Fixed Point ◽  
Tensor Product ◽  
Cartesian Product ◽  
Matrix Equations ◽  
Minimum Cardinality ◽  
Sylvester Matrix ◽  
Product Graphs ◽  
Cartesian Product Graphs ◽  
Sylvester Matrix Equations ◽  
Point Type

This paper extends the concept of tropical tensor product defined by Butkovic and Fiedler to general idempotent dioids. Then, it proposes an algorithm in order to solve the fixed-point type Sylvester matrix equations of the form X = A ⊗ X ⊕ X ⊗ B ⊕ C. An application is discussed in efficiently solving the minimum cardinality path problem in Cartesian product graphs.

scholarly journals Tensor Product Of Zero-divisor Graphs With Finite Free Semilattices

2017 ◽  
Vol 9 (1) ◽  
pp. 13
Author(s):  
Kemal Toker
Keyword(s):  
Tensor Product ◽  
Chromatic Number ◽  
Zero Divisor ◽  
Independence Number ◽  
Domination Number ◽  
Clique Number ◽  
Perfect Graph ◽  
Chromatic Index

$\Gamma (SL_{X})$ is defined and has been investigated in (Toker, 2016). In this paper our main aim is to extend this study over  $\Gamma (SL_{X})$ to the tensor product. The diameter, radius, girth, domination number, independence number, clique number, chromatic number and chromatic index of $\Gamma (SL_{X_{1}})\otimes \Gamma (SL_{X_{2}})$ has been established. Moreover, we have determined when $\Gamma (SL_{X_{1}})\otimes \Gamma (SL_{X_{2}})$ is a perfect graph.

scholarly journals On the independence and domination numbers of replacement product graphs

2016 ◽  
Vol 9 (2) ◽  
pp. 181-194
Author(s):  
Jay Cummings ◽  
Christine A. Kelley
Keyword(s):  
Product Graphs ◽  
Replacement Product ◽  
Domination Numbers

scholarly journals On the domination and signed domination numbers of zero-divisor graph

2016 ◽  
Vol 1 (2) ◽  
pp. 148-156
Author(s):  
Ebrahim Vatandoost ◽  
◽  
Fatemeh Ramezani
Keyword(s):  
Zero Divisor ◽  
Zero Divisor Graph ◽  
Signed Domination ◽  
Domination Numbers

scholarly journals On tensor product graphs

1975 ◽  
Vol 20 (3) ◽  
pp. 268-273 ◽  
Author(s):  
E. Sampathkumar
Keyword(s):  
Tensor Product ◽  
Product Graphs ◽  
Point Set

AbstractThe tensor product G ⊕ H of graphs G and H is the graph with point set V(G) × V(H) where (υ1, ν1) adj (υ2, ν2) if, and only if, u1 adj υ2 and ν1 adj ν2. We obtain a characterization of graphs of the form G ⊕ H where G or H is K2.

scholarly journals Tensor products and localizations of algebras

1986 ◽  
Vol 102 ◽  
pp. 155-161 ◽  
Author(s):  
S. R. Bowman ◽  
L. O’Carroll
Keyword(s):  
Tensor Product ◽  
Prime Ideal ◽  
Finite Number ◽  
Nilpotent Element ◽  
Zero Divisor ◽  
Tensor Products ◽  
Associated Primes ◽  
Primary Ring

In a recent paper [5], it was shown that the tensor product of a finite number of fields over a common subfield satisfies the property that each localization at a prime ideal is a primary ring (in the sense that a zero-divisor is in fact a nilpotent element).In the first section of this paper, we exploit the properties of associated primes and of flat extensions so as to generalize the above result to zero-dimensional algebras; a simple example shows that this is the best one can hope for. The converse situation is also investigated.

On Some Topological Indices of Tensor Product Graphs

2018 ◽  
Vol 64 (1) ◽  
pp. 37-45
Author(s):  
K.V.S.Sa rma ◽  
◽  
I.V.N Uma ◽  
I.H.N Rao
Keyword(s):  
Tensor Product ◽  
Topological Indices ◽  
Product Graphs
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