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

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.

BOUNDS OF TOPOLOGICAL INDICES OF TENSOR PRODUCT OF GRAPH OPERATIONS

2017 ◽  
Vol 102 (12) ◽  
pp. 3067-3091
Author(s):  
Muhammad Imran ◽  
Shakila Baby ◽  
Hafiz Muhammad Afzal Siddiqui ◽  
Muhammad Kashif Shafiq
Keyword(s):  
Tensor Product ◽  
Topological Indices ◽  
Graph Operations

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.

On degree-based topological descriptors of strong product graphs

2016 ◽  
Vol 94 (6) ◽  
pp. 559-565 ◽  
Author(s):  
Shehnaz Akhter ◽  
Muhammad Imran
Keyword(s):  
Physicochemical Properties ◽  
Strain Energy ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Topological Descriptors ◽  
Zagreb Indices ◽  
Strong Product ◽  
Product Graphs ◽  
Product Of Graphs ◽  
Atom Bond

Topological descriptors are numerical parameters of a graph that characterize its topology and are usually graph invariant. In a QSAR/QSPR study, physicochemical properties and topological indices such as Randić, atom–bond connectivity, and geometric–arithmetic are used to predict the bioactivity of different chemical compounds. There are certain types of topological descriptors such as degree-based topological indices, distance-based topological indices, counting-related topological indices, etc. Among degree-based topological indices, the so-called atom–bond connectivity and geometric–arithmetic are of vital importance. These topological indices correlate certain physicochemical properties such as boiling point, stability, strain energy, etc., of chemical compounds. In this paper, analytical closed formulas for Zagreb indices, multiplicative Zagreb indices, harmonic index, and sum-connectivity index of the strong product of graphs are determined.

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.

scholarly journals Computing Certain Topological Indices of the Line Graphs of Subdivision Graphs of Some Rooted Product Graphs

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 393 ◽  
Author(s):  
Adnan Aslam ◽  
Muhammad Faisal Nadeem ◽  
Zohaib Zahid ◽  
Sohail Zafar ◽  
Wei Gao
Keyword(s):  
Topological Indices ◽  
Topological Invariants ◽  
Line Graphs ◽  
Product Graph ◽  
Product Graphs

In this work, we study the degree-based topological invariants, and the general sum-connectivity, A B C 4 , G A 5 , general Zagreb, G A , generalized Randić, and A B C indices of the line graphs of some rooted product graphs ( C n { P k } and C n { S m + 1 } ) are determined by menas of the concept of subdivision. Moreover, we also computed all these indices of the line graphs of the subdivision graphs of i-th vertex rooted product graph C i , r { P k + 1 } .

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 On the Hyper-Zagreb Index of Some Graph Binary Operations

2020 ◽  
pp. 12-24
Author(s):  
Mohammed Saad Yahya Al-Sharafi ◽  
Mahioub Mohammed Shubatah
Keyword(s):  
Graph Theory ◽  
Tensor Product ◽  
Topological Indices ◽  
Symmetric Difference ◽  
Zagreb Index ◽  
Binary Operations

This study looked at Graph theory as it is an important part of mathematics. Topological indices are numerical parameters of a graph which describe its structure, they have many applications as tools for modeling chemical and other properties of molecules. In this paper, we presented some exact formulas of the Hyper-Zagreb index for some special graphs and some graph binary operations such disjunction G v H, symmetric difference G H, and tensor product G H of graphs.

Bounds for General Connectivity Indices of Tensor Product of Connected Graphs

2018 ◽  
Author(s):  
Shakila Baby ◽  
Muhammad Kashif Shafiq ◽  
Asim Naseem ◽  
Hafiz Muhammad Afzal Siddiqui
Keyword(s):  
Tensor Product ◽  
Topological Indices ◽  
Graph Invariant ◽  
Connected Graphs ◽  
Connectivity Indices ◽  
Product Of Graphs

Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In this paper, bounds for the Randić, general Randić, sum-connectivity, the general sum-connectivity and harmonic indices for tensor product of graphs are determined by using the combinatorial inequalities and combinatorial computing.

Reference Signal Based Tensor Product Expansion for EOG-Related Artifact Separation in EEG

2017 ◽  
Vol E100.A (11) ◽  
pp. 2230-2237
Author(s):  
Akitoshi ITAI ◽  
Arao FUNASE ◽  
Andrzej CICHOCKI ◽  
Hiroshi YASUKAWA
Keyword(s):  
Tensor Product ◽  
Reference Signal
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