Hyper-connectivity index for fuzzy graph with application

Connectivity concept is one of the most important parameters in fuzzy graphs (FGs). The stability of a FG is dependent on the strength of connectedness between each pair of vertices. Depending on “strength of connectedness between each pair of vertices” hyper-connectivity index for fuzzy graph (FHCI) is introduced and studied this index for various FGs like partial fuzzy subgraph, fuzzy subgraph, complete fuzzy graph, saturated cycle, isomorphic fuzzy graphs, etc. A relation of FHCI is established between fuzzy graph and partial fuzzy subgraph. Also, a relation between FHCI and connectivity index for fuzzy graph (FCI) is provided. In the end of the article, a decision-making problem is presented and solved it by using FHCI. Also, a comparison is provided among related indices on the result of application and shown that our method gives better result.Publisher's Versio

A Survey of Operations Research and Analytics Literature Related to Anti-Human Trafficking

Human trafficking is a compound social, economic, and human rights issue occurring in all regions of the world. Understanding and addressing such a complex crime requires effort from multiple domains and perspectives. As of this writing, no systematic review exists of the Operations Research and Analytics literature applied to the domain of human trafficking. The purpose of this work is to fill this gap through a systematic literature review. Studies matching our search criteria were found ranging from 2010 to March 2021. These studies were gathered and analyzed to help answer the following three research questions: (i) What aspects of human trafficking are being studied by Operations Research and Analytics researchers? (ii) What Operations Research and Analytics methods are being applied in the anti-human trafficking domain? and (iii) What are the existing research gaps associated with (i) and (ii)? By answering these questions, we illuminate the extent to which these topics have been addressed in the literature, as well as inform future research opportunities in applying analytical methods to advance the fight against human trafficking.Comment: 28 pages, 6 Figures, 2 Table

F-index for fuzzy graph with application

The first author is supported by University Grant Commission (UGC) Govt. of India under UGC-Ref. No.: 1144/ (CSIR-UGC NET JUNE 2017) dated 26/12/2018.Different types of topological index of a graph have many applications and many results are available for crisp graphs. But in many practical applications it is seen that many situations cannot be modeled using crisp graphs. In these cases, to handle such a situation, those topological indices are needed to define in a fuzzy graph. In this article, F-index for fuzzy graphs is introduced and some bounds on F-index are provided for several fuzzy graphs such as path, cycle, star, complete fuzzy graph, etc. In this article, the maximal fuzzy graph is calculated with respect to the F-index for a given vertex set. At the end of this article, a group of researchers are considered and a decision making method is provided by using F-index for fuzzy graph to find the most influenced researcher in that group.Publisher's Versio

Constant single valued neutrosophic graphs with applications

In this paper, we introduced a new concept of single valued neutrosophic graph (SVNG) known as constant single valued neutrosophic graph (CSVNG). Basically, SVNG is a generalization of intuitionistic fuzzy graph (IFG). More specifically, we described and explored somegraph theoretic ideas related to the introduced concepts of CSVNG. An application of CSVNG in a Wi-Fi network system is discussed and a comparison of CSVNG with constant IFG is established showing the worth of the proposed work. Further, several terms like constant function and totally constant function are investigated in the frame-work of CSVNG and their characteristics are studied

Pythagorean fuzzy incidence graphs with application in illegal wildlife trade

Chemical engineers can model numerous interactions in a process using incidence graphs. They are used to methodically map out a whole network of interconnected processes and controllers to describe each component's impact on the others. It makes it easier to visualize potential process paths or a series of impacts. A Pythagorean fuzzy set is an effective tool to overcome ambiguity and vagueness. In this paper, we introduce the concept of Pythagorean fuzzy incidence graphs. We discuss the incidence path and characterize the strongest incidence path in Pythagorean fuzzy incidence graphs. Furthermore, we propose the idea of Pythagorean fuzzy incidence cycles and Pythagorean fuzzy incidence trees in Pythagorean fuzzy incidence graphs and give some essential results. We illustrate the notions of Pythagorean fuzzy incidence cut vertices, Pythagorean fuzzy incidence bridges, and Pythagorean fuzzy incidence cut pairs. We also establish some results about Pythagorean fuzzy incidence cut pairs. Moreover, we study the types of incidence pairs and determine some crucial results concerning strong incidence pairs in the Pythagorean fuzzy incidence graph. We also obtain the characterization of Pythagorean fuzzy incidence cut pairs using $\alpha$-strong incidence pairs and find the relation between Pythagorean fuzzy incidence trees and $\alpha$-strong incidence pairs. Finally, we provide the application of Pythagorean fuzzy incidence graphs in the illegal wildlife trade

Constant single valued neutrosophic graphs with applications

In this paper, we introduced a new concept of single valued neutrosophic graph (SVNG) known as constant single valued neutrosophic graph (CSVNG). Basically, SVNG is a generalization of intuitionistic fuzzy graph (IFG). More specifically, we described and explored somegraph theoretic ideas related to the introduced concepts of CSVNG. An application of CSVNG in a Wi-Fi network system is discussed and a comparison of CSVNG with constant IFG is established showing the worth of the proposed work. Further, several terms like constant function and totally constant function are investigated in the frame-work of CSVNG and their characteristics are studied

Connectivity index in neutrosophic trees and the algorithm to find its maximum spanning

In this paper, we first define the Neutrosophic tree using the concept of the strong cycle. We then define a strong spanning Neutrosophic tree. In the following, we propose an algorithm for detecting the maximum spanning tree in Neutrosophic graphs. Next, we discuss the Connectivity index and related theorems for Neutrosophic trees

Improving Computer Network Operations Through Automated Interpretation of State

Networked systems today are hyper-scaled entities that provide core functionality for distributed services and applications spanning personal, business, and government use. It is critical to maintain correct operation of these networks to avoid adverse business outcomes. The advent of programmable networks has provided much needed fine-grained network control, enabling providers and operators alike to build some innovative networking architectures and solutions. At the same time, they have given rise to new challenges in network management. These architectures, coupled with a multitude of devices, protocols, virtual overlays on top of physical data-plane etc. make network management a highly challenging task. Existing network management methodologies have not evolved at the same pace as the technologies and architectures. Current network management practices do not provide adequate solutions for highly dynamic, programmable environments. We have a long way to go in developing management methodologies that can meaningfully contribute to networks becoming self-healing entities. The goal of my research is to contribute to the design and development of networks towards transforming them into self-healing entities. Network management includes a multitude of tasks, not limited to diagnosis and troubleshooting, but also performance engineering and tuning, security analysis etc. This research explores novel methods of utilizing network state to enhance networking capabilities. It is constructed around hypotheses based on careful analysis of practical deficiencies in the field. I try to generate real-world impact with my research by tackling problems that are prevalent in deployed networks, and that bear practical relevance to the current state of networking. The overarching goal of this body of work is to examine various approaches that could help enhance network management paradigms, providing administrators with a better understanding of the underlying state of the network, thus leading to more informed decision-making. The research looks into two distinct areas of network management, troubleshooting and routing, presenting novel approaches to accomplishing certain goals in each of these areas, demonstrating that they can indeed enhance the network management experience