Maximal Product of Graphs under Vague Environment

Hoseini, B. Sheikh; Akram, Muhammad; Hosseini, Mehrnaz Sheikh; Rashmanlou, Hossein; Borzooei, Rajab Ali

doi:10.3390/mca25010010

Cited by 3 publications

(1 citation statement)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…GSs are very useful in the study of different domains of computer science and computational intelligence. Borzoei and Rashmanlou [21] presented the concept of the maximal product of graphs under a vague environment. Akram et al [22][23][24] investigated certain types of vague cycles, vague trees, and Cayley vague graphs.…”

Section: Introductionmentioning

confidence: 99%

Energy of Vague Fuzzy Graph Structure and Its Application in Decision Making

Wan

Talebi

et al. 2022

Symmetry

View full text Add to dashboard Cite

Vague graphs (VGs), belonging to the fuzzy graphs (FGs) family, have good capabilities when faced with problems that cannot be expressed by FGs. The notion of a VG is a new mathematical attitude to model the ambiguity and uncertainty in decision-making issues. A vague fuzzy graph structure (VFGS) is the generalization of the VG. It is a powerful and useful tool to find the influential person in various relations. VFGSs can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problems where fuzzy graphs may fail to reveal satisfactory results. Moreover, VGSs are very useful tools for the study of different domains of computer science such as networking, social systems, and other issues such as bioscience and medical science. The subject of energy in graph theory is one of the most attractive topics that is very important in biological and chemical sciences. Hence, in this work, we extend the notion of energy of a VG to the energy of a VFGS and also use the concept of energy in modeling problems related to VFGS. Actually, our purpose is to develop a notion of VFGS and investigate energy and Laplacian energy (LE) on this graph. We define the adjacency matrix (AM) concept, energy, and LE of a VFGS. Finally, we present three applications of the energy in decision-making problems.

show abstract

Section: Introductionmentioning

confidence: 99%

Energy of Vague Fuzzy Graph Structure and Its Application in Decision Making

Wan

Talebi

et al. 2022

Symmetry

View full text Add to dashboard Cite

show abstract

Novel Concepts in Vague Graphs with Application in Hospital’s Management System

Kosari

Muhiuddin

2022

Journal of Mathematics

View full text Add to dashboard Cite

Many problems of practical interest can be modeled and solved by using vague graph (VG) algorithms. Vague graphs, belonging to the fuzzy graphs (FGs) family, have good capabilities when faced with problems that cannot be expressed by FGs. Hence, in this paper, we introduce the notion of η , γ - HMs of VGs and classify homomorphisms (HMs), weak isomorphisms (WIs), and coweak isomorphisms (CWIs) of VGs by η , γ - HMs. Hospitals are very important organizations whose existence is directly related to the general health of the community. Hence, since the management in each ward of the hospital is very important, we have tried to determine the most effective person in a hospital based on the performance of its staff.

show abstract

A Survey on Domination in Vague Graphs with Application in Transferring Cancer Patients between Countries

Rao

Chen

et al. 2021

Mathematics

View full text Add to dashboard Cite

Many problems of practical interest can be modeled and solved by using fuzzy graph (FG) algorithms. In general, fuzzy graph theory has a wide range of application in various fields. Since indeterminate information is an essential real-life problem and is often uncertain, modeling these problems based on FG is highly demanding for an expert. A vague graph (VG) can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems in which fuzzy graphs may not succeed in bringing about satisfactory results. Domination in FGs theory is one of the most widely used concepts in various sciences, including psychology, computer sciences, nervous systems, artificial intelligence, decision-making theory, etc. Many research studies today are trying to find other applications for domination in their field of interest. Hence, in this paper, we introduce different kinds of domination sets, such as the edge dominating set (EDS), the total edge dominating set (TEDS), the global dominating set (GDS), and the restrained dominating set (RDS), in product vague graphs (PVGs) and try to represent the properties of each by giving some examples. The relation between independent edge sets (IESs) and edge covering sets (ECSs) are established. Moreover, we derive the necessary and sufficient conditions for an edge dominating set to be minimal and show when a dominance set can be a global dominance set. Finally, we try to explain the relationship between a restrained dominating set and a restrained independent set with an example. Today, we see that there are still diseases that can only be treated in certain countries because they require a long treatment period with special medical devices. One of these diseases is leukemia, which severely affects the immune system and the body’s defenses, making it impossible for the patient to continue living a normal life. Therefore, in this paper, using a dominating set, we try to categorize countries that are in a more favorable position in terms of medical facilities, so that we can transfer the patients to a suitable hospital in the countries better suited in terms of both cost and distance.

show abstract

Maximal Product of Graphs under Vague Environment

Cited by 3 publications

References 17 publications

Energy of Vague Fuzzy Graph Structure and Its Application in Decision Making

Energy of Vague Fuzzy Graph Structure and Its Application in Decision Making

Novel Concepts in Vague Graphs with Application in Hospital’s Management System

A Survey on Domination in Vague Graphs with Application in Transferring Cancer Patients between Countries

Contact Info

Product

Resources

About