Mappings of Cubic Sets

Kang, Jeong Gi

doi:10.4134/ckms.c150148

Cited by 14 publications

(8 citation statements)

References 5 publications

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“…One of the genuine speculations of fuzzy sets is the cubic set given by Jun et al [24] during the most recent 5 years. Mappings of cubic sets were concentrated by Kang and Kim [25]. Stable cubic sets were presented by Muhiuddin et al [26].…”

Section: Introductionmentioning

confidence: 99%

Cubic Planar Graph and Its Application to Road Network

Muhiuddin

Hameed

Rasheed

et al. 2022

Mathematical Problems in Engineering

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In this research article, we present the notion of a cubic planar graph and investigate its related properties. The cubic graphs are more effective than both interval-valued and fuzzy graphs as it represents the level of participation (membership degree) of vertices and edges both in interval form and as a fuzzy number. Moreover, it handles the uncertainty and vagueness more efficiently than both interval-valued fuzzy graph and fuzzy graph. The interval indicates a continuous process, whereas the point indicates a specific process. We introduce the terms cubic multigraph, cubic strong and weak edges, and degree of planarity for cubic planar graphs. Some fundamental theorems based on these concepts are also elaborated. We also propose the idea of a cubic strong and weak fuzzy faces and cubic dual graph. Some results related to these concepts are also established. Comparison with the existing method shows the worth of our proposed work.

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Section: Introductionmentioning

confidence: 99%

Cubic Planar Graph and Its Application to Road Network

Muhiuddin

Hameed

Rasheed

et al. 2022

Mathematical Problems in Engineering

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“…Aided by his colleagues, he also applied this concept to algebraic structures [35][36][37][38]. Kang and Kim [39] investigated CSs mappings. Muhiuddin et al [40] presented the stable CSs idea.…”

Section: Introductionmentioning

confidence: 99%

New Concepts of Vertex Covering in Cubic Graphs with Its Applications

et al. 2022

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Graphs serve as one of the main tools for the mathematical modeling of various human problems. Fuzzy graphs have the ability to solve uncertain and ambiguous problems. The cubic graph, which has recently gained a position in the fuzzy graph family, has shown good capabilities when faced with problems that cannot be expressed by fuzzy graphs and interval-valued fuzzy graphs. Simultaneous application of fuzzy and interval-valued fuzzy membership indicates a high flexibility in modeling uncertainty issues. The vertex cover is a fundamental issue in graph theory that has wide application in the real world. The previous definition limitations in the vertex covering of fuzzy graphs has directed us to offer new classifications in terms of cubic graph. In this study, we introduced the strong vertex covering and independent vertex covering in a cubic graph with strong edges and described some of its properties. One of the motives of this research was to examine the changes in the strong vertex covering number of a cubic graph if one vertex is omitted. This issue can play a decisive role in covering the graph vertices. Since many of the problems ahead are of hybrid type, by reviewing some operations on the cubic graph we were able to determine the strong vertex covering number on the most important cubic product operations. Finally, two applications of strong vertex covering and strong vertex independence are presented.

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“…For more detail of cubic set one can cite [6]- [11]. More recently Jun et al combine neutrosophic set with cubic sets and gave the idea of Neutrosophic cubic set [12] and define different operations [13]. Further interval neutrosophic sets was introduced by Jun et al [14].…”

Section: Introductionmentioning

confidence: 99%

Novel Neutrosophic Cubic Graphs Structures With Application in Decision Making Problems

et al. 2019

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Graphs allow us to study the different patterns of inside the data by making a mental image. The aim of this paper is to develop a neutrosophic cubic graph structure, which is the extension of neutrosophic cubic graphs. As neutrosophic cubic graphs are defined for one set of edges between vertices, while neutrosophic cubic graphs structures are defined for more than one set of edges. Further, we defined some basic operations, such as Cartesian product, composition, union, join, cross product, strong product, and lexicographic product of two neutrosophic cubic graph structures. Several types of other interesting properties of neutrosophic cubic graph structures are discussed in this paper. Finally, a decisionmaking algorithm based on the idea of neutrosophic cubic graph structures is constructed. The proposed decision-making algorithm is applied in a decision-making problem to check the validity.

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Mappings of Cubic Sets

Cited by 14 publications

References 5 publications

Cubic Planar Graph and Its Application to Road Network

Cubic Planar Graph and Its Application to Road Network

New Concepts of Vertex Covering in Cubic Graphs with Its Applications

Novel Neutrosophic Cubic Graphs Structures With Application in Decision Making Problems

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