Abstract
Fuzzy graphs (FGs), broadly known as fuzzy incidence graphs (FIGs), have been acknowledged as being an applicable and well-organized tool to epitomize and solve many multifarious real-world problems in which vague data and information are essential. Owing to unpredictable and unspecified information being an integral component in real-life problems that are often uncertain, it is highly challenging for an expert to illustrate those problems through a fuzzy graph. Therefore, resolving the uncertainty accompanying the unpredictable and unspecified information of any real-world problem can be done by applying a vague incidence graph (VIG), based on which the FGs may not engender satisfactory results. Similarly, VIGs are outstandingly practical tools for analyzing different computer science domains such as networking, clustering, and also other issues such as medical sciences, and traffic planning. Dominating sets (DSs) enjoy practical interest in several areas. In wireless networking, DSs are being used to find efficient routes with ad-hoc mobile networks. They have also been employed in document summarization, and in secure systems designs for electrical grids; consequently, in this paper, we extend the concept of the FIG to the VIG, and show some of its important properties. In particular, we discuss the well-known problems of vague incidence dominating set, valid degree, isolated vertex, vague incidence irredundant set and their cardinalities related to the dominating, etc. Finally, a DS application for VIG to properly manage the COVID-19 testing facility is introduced.
Highlights
The graph concept stands as one of the most dominant and widely employed tools for the multiple real-world problem representation, modeling, and analyses
Fuzzy set theory was required to contend with many multidimensional issues, which are replete with incomplete information
In this research, we extend the concept of the fuzzy incidence graphs (FIGs) to the vague incidence graph (VIG) and discuss the well-known problems of vague incidence dominating set (VIDS), valid degree, vague incidence irredundant set (VIIS), and their cardinalities related to the domination, etc
Summary
The graph concept stands as one of the most dominant and widely employed tools for the multiple real-world problem representation, modeling, and analyses. Fuzzy set theory is a highly influential mathematical tool for solving approximate reasoning related problems. Rashmanlou et al [28,29,30,31] introduced new concepts in VGs. Domination in graphs has many applications to several fields. Described the concept of a domination number in an intuitionistic fuzzy graph. Notably Talebi and Rashmanlou [35], studied new applications of the concept of domination in VGs. The vague incidence model is more compliant and functioning than fuzzy and intuitionistic incidence fuzzy models. The vague incidence model is more compliant and functioning than fuzzy and intuitionistic incidence fuzzy models In several applications, such as urban traffic planning, telecommunication message routing, very large-scale integration chip optimal pipelining, etc., VIGs serve as the observed real-world systems mathematical models. An application of DS for VIG to properly manage the COVID-19 testing facility is introduced
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