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.

scholarly journals Application of Bipolar Fuzzy Sets in Graph Structures

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Muhammad Akram ◽  
Rabia Akmal
Keyword(s):  
Computer Science ◽  
Fuzzy Sets ◽  
Computational Intelligence ◽  
Combinatorial Problems ◽  
Graph Structure ◽  
Fuzzy Graph ◽  
Cut Vertex ◽  
Graph Structures ◽  
Bipolar Fuzzy Sets

A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we apply the concept of bipolar fuzzy sets to graph structures. We introduce certain notions, including bipolar fuzzy graph structure (BFGS), strong bipolar fuzzy graph structure, bipolar fuzzyNi-cycle, bipolar fuzzyNi-tree, bipolar fuzzyNi-cut vertex, and bipolar fuzzyNi-bridge, and illustrate these notions by several examples. We studyϕ-complement, self-complement, strong self-complement, and totally strong self-complement in bipolar fuzzy graph structures, and we investigate some of their interesting properties.

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 Number of Spanning Trees of Different Products of Complete and Complete Bipartite Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-23 ◽  
Author(s):  
S. N. Daoud
Keyword(s):  
Tensor Product ◽  
Linear Algebra ◽  
Spanning Trees ◽  
Matrix Theory ◽  
Cartesian Product ◽  
Bipartite Graphs ◽  
Normal Product ◽  
Complete Bipartite Graphs ◽  
Composition Product ◽  
Number Of Spanning Trees

Spanning trees have been found to be structures of paramount importance in both theoretical and practical problems. In this paper we derive new formulas for the complexity, number of spanning trees, of some products of complete and complete bipartite graphs such as Cartesian product, normal product, composition product, tensor product, symmetric product, and strong sum, using linear algebra and matrix theory techniques.

scholarly journals The generalized 3-connectivity of Cartesian product graphs

2012 ◽  
Vol Vol. 14 no. 1 (Graph Theory) ◽  
Author(s):  
Hengzhe Li ◽  
Xueliang Li ◽  
Yuefang Sun
Keyword(s):  
Graph Theory ◽  
Positive Integer ◽  
Cartesian Product ◽  
Vertex Connectivity ◽  
Connected Graphs ◽  
Generalized Connectivity ◽  
Product Graphs ◽  
International Audience ◽  
Cartesian Product Graphs ◽  
Internally Disjoint Trees

Graph Theory International audience The generalized connectivity of a graph, which was introduced by Chartrand et al. in 1984, is a generalization of the concept of vertex connectivity. Let S be a nonempty set of vertices of G, a collection \T-1, T (2), ... , T-r\ of trees in G is said to be internally disjoint trees connecting S if E(T-i) boolean AND E(T-j) - empty set and V (T-i) boolean AND V(T-j) = S for any pair of distinct integers i, j, where 1 <= i, j <= r. For an integer k with 2 <= k <= n, the k-connectivity kappa(k) (G) of G is the greatest positive integer r for which G contains at least r internally disjoint trees connecting S for any set S of k vertices of G. Obviously, kappa(2)(G) = kappa(G) is the connectivity of G. Sabidussi's Theorem showed that kappa(G square H) >= kappa(G) + kappa(H) for any two connected graphs G and H. In this paper, we prove that for any two connected graphs G and H with kappa(3) (G) >= kappa(3) (H), if kappa(G) > kappa(3) (G), then kappa(3) (G square H) >= kappa(3) (G) + kappa(3) (H); if kappa(G) = kappa(3)(G), then kappa(3)(G square H) >= kappa(3)(G) + kappa(3) (H) - 1. Our result could be seen as an extension of Sabidussi's Theorem. Moreover, all the bounds are sharp.

scholarly journals Adjacency Matrix of Product of Graphs

10.29007/fqlw ◽  
2018 ◽  
Author(s):  
Urvashi Acharya ◽  
Himali Mehta
Keyword(s):  
Graph Theory ◽  
Tensor Product ◽  
Adjacency Matrix ◽  
Incidence Matrix ◽  
Cartesian Product ◽  
Laplacian Matrix ◽  
New Product ◽  
Different Types ◽  
Product Of Graphs

In graph theory, different types of matrices associated with graph, e.g. Adjacency matrix, Incidence matrix, Laplacian matrix etc. Among all adjacency matrix play an important role in graph theory. Many products of two graphs as well as its generalized form had been studied, e.g., cartesian product, 2−cartesian product, tensor product, 2−tensor product etc. In this paper, we discuss the adjacency matrix of two new product of graphs G H, where = ⊗2, ×2. Also, we obtain the spectrum of these products of graphs.

scholarly journals The generalized 3-connectivity of Lexicographic product graphs

2014 ◽  
Vol Vol. 16 no. 1 (Graph Theory) ◽  
Author(s):  
Xueliang Li ◽  
Yaping Mao
Keyword(s):  
Graph Theory ◽  
Cartesian Product ◽  
Natural Generalization ◽  
Upper Bounds ◽  
Lexicographic Product ◽  
Vertex Connectivity ◽  
Connected Graphs ◽  
Product Graphs ◽  
International Audience ◽  
Lexicographic Product Graphs

Graph Theory International audience The generalized k-connectivity κk(G) of a graph G, first introduced by Hager, is a natural generalization of the concept of (vertex-)connectivity. Denote by G^H and G&Box;H the lexicographic product and Cartesian product of two graphs G and H, respectively. In this paper, we prove that for any two connected graphs G and H, κ3(G^H)&#x2265; κ3(G)|V(H)|. We also give upper bounds for κ3(G&Box; H) and κ3(G^H). Moreover, all the bounds are sharp.

scholarly journals An Application of Product of Intuitionistic Fuzzy Incidence Graphs in Textile Industry

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Irfan Nazeer ◽  
Tabasam Rashid ◽  
Abazar Keikha
Keyword(s):  
Comparative Analysis ◽  
Tensor Product ◽  
Textile Industry ◽  
Cartesian Product ◽  
Normal Product ◽  
Maximum Percentage ◽  
Intuitionistic Fuzzy ◽  
Research Article ◽  
Garment Factories

In this research article, we presented the idea of intuitionistic fuzzy incidence graphs (IFIGs) along with their certain properties. The number of operations including Cartesian product (CP), composition, tensor product, and normal product in an IFIGs are also investigated. The method to compute the degree of IFIGs obtained by CP, composition, tensor product, and the normal product is discussed. Some important theorems to calculate the degree of the vertices of IFIGs acquired by CP, composition, tensor product, and normal product are elaborated. An application of CP and composition of two IFIGs in the textile industry to find the best combinations of departments expressing the highest percentage of progress and the lowest percentage of nonprogress is provided. A comparative analysis of our study with the existing study is discussed. Our study will be beneficial to comprehend and understand the further characteristics of IFIGs in detail. Another advantage of our study is that it will be helpful to find the maximum percentage of progress and minimum percentage of nonprogress in different departments of universities, garment factories, and hospitals.

scholarly journals Complexity of Products of Some Complete and Complete Bipartite Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-25 ◽  
Author(s):  
S. N. Daoud
Keyword(s):  
Tensor Product ◽  
Spanning Trees ◽  
Cartesian Product ◽  
Bipartite Graphs ◽  
Matrix Analysis ◽  
Normal Product ◽  
Analysis Techniques ◽  
Complete Bipartite Graphs ◽  
Composition Product ◽  
Number Of Spanning Trees

The number of spanning trees in graphs (networks) is an important invariant; it is also an important measure of reliability of a network. In this paper, we derive simple formulas of the complexity, number of spanning trees, of products of some complete and complete bipartite graphs such as cartesian product, normal product, composition product, tensor product, and symmetric product, using linear algebra and matrix analysis techniques.

scholarly journals Signless Laplacian Energy in Products of Intuitionistic Fuzzy Graphs

2019 ◽  
Vol 8 (3) ◽  
pp. 8536-8545
Keyword(s):  
Tensor Product ◽  
Cartesian Product ◽  
Fuzzy Graph ◽  
Lexicographic Product ◽  
Intuitionistic Fuzzy ◽  
Strong Product ◽  
Fuzzy Graphs ◽  
Laplacian Energy ◽  
Signless Laplacian ◽  
Intuitionistic Fuzzy Graphs

The observation of an Intuitionistic Fuzzy Graph’s signless laplacian energy is expanded innumerous products in Intuitionistic Fuzzy Graph. During this paper, we have got the value of signless laplacian Energy in unrelated products such as Cartesian product, Lexicographic Product, Tensor product and Strong Product, product, product and product amongst 2 intuitionistic Fuzzy graphs. Additionally we tend to study the relation between the Signless laplacian Energy within the varied products in 2 Intuitionistic Fuzzy Graphs

Fuzzy graph theory in coloring graph

2021 ◽  
Author(s):  
S. Sangeetha ◽  
P. Hema ◽  
N. Selvarani ◽  
P. Geetha ◽  
P. Karthikeyan ◽  
...  
Keyword(s):  
Graph Theory ◽  
Fuzzy Graph ◽  
Coloring Graph
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