• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.341-354
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• 2016

In this paper, the exact formulae for the generalized product degree distance, reciprocal product degree distance and product degree distance of tensor product of a connected graph and the complete multipartite graph with partite sets of sizes m₀, m₁, ⋯ , m_r−1 are obtained.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.527-544
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• 1999

The generalized Hardie-Jansen product and its dual are defined and the fundamental results on these products are obtained. By studying the adjoint maps, we give proofs to them. Moreover we characterize the generalized Hardie-jansen product making use of the ${\Gamma}W$-Whitehead product. We also obtain a characterization of the dual of the generalized Hardie-Jansen product using $({\Gamma}W)$-Whitehead product.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.283-290
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• 2024

In this article, a new operation on product fuzzy graphs (PFGs) is provide; namely β-product. We give sufficient conditions for the β-product of two PFGs to be strong and we prove if the β-product of two PFGs is complete, then one of them is strong. We also study the unbiased notion of the class of PFGs and necessary and sufficient conditions for the β-product to be unbiased are given.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.883-899
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• 2014

We introduce GCR-lightlike submanifold of a semi-Riemannian product manifold and give an example. We study geodesic GCR-lightlike submanifolds of a semi-Riemannian product manifold and obtain some necessary and sufficient conditions for a GCR-lightlike submanifold to be a GCR-lightlike product. Finally, we discuss minimal GCR-lightlike submanifolds of a semi-Riemannian product manifold.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.1145-1153
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• 2023

The notion of maximal product of two fuzzy graphs was introduced by Radha and Arumugam in 2015 and the notion of balanced fuzzy graph was introduced by Al-Hawary in 2011. In this paper, we give a modification of the maximal product definition, which we call maximal strong product. We also introduce the relatively new notion of maximal-balanced fuzzy graphs. We give necessary and sufficient conditions for the maximal strong product of two balanced (resp., maximal-balanced) fuzzy graphs to be balanced (resp., maximal-balanced) and we prove that these two independent notions are preserved under isomorphism.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.2
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• pp.53-61
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• 2001

We introduce sums and joins of fuzzy finite state machines and investigate their algebraic structures.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.469-477
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• 2013

Pattabiraman and Paulraja [K. Pattabiraman, P. Paulraja, Vertex and edge PI indices of the generalized hierarchical product of graphs, Discrete Appl. Math. 160 (2012) 1376- 1384] obtained exact formulas for the vertex and edge PI indices of generalized hierarchical product of graphs. The aim of this note is to improve the main results of this paper.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.705-716
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• 2002

In this paper we shall introduce the algebraic structure of a tensor product for arbitrarily given automata, giving a defintion of the tensor product for automata. We introduce and study that for any set X there always exists a free automaton on X. The existence of a tensor product for automata will be investigated in the same way like modules do.

• Journal of the Ergonomics Society of Korea
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• v.27 no.2
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• pp.15-24
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• 2008

As users increasingly recognize the importance of safety and the Product Liability comes into effect, a company should take responsibility of protecting the users who use its product. In order to produce a safe product and satisfy the needs of users, it is critical for develope opriately and understand the characteristics of the product accurately. Furthermore, a safe product can be realized by considering a safety level of the product in a whole product development process. However, in general, product development projects hardly evaluate the safety of a product in the product planning step. In addition, most of safety evaluation methods which are applied in the product planning step have a tendency to be qualitative because a detailed product design step. Therefore, this research aims at enhancing the performance of the safety evaluation process by applying quantitative methods such as 'AHP' and 'Fuzzy'. AHP can help analysts derive the weight of safety factors. Fuzzy is applied to evaluate the degree of safety of product elements in this paper. The proposed method will be able to improve the safety level of a product by using the quantitative methods in the product planning step.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.385-390
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• 2003

In this paper, we are going to study the twisted product manifold in connection with conharmonic transformation.