Domination of Bipolar Fuzzy Graphs in Various Settings

Abstract

Bipolar fuzzy sets are used to describe the positive and negative of the uncertainty of objects, and the bipolar fuzzy graphs are used to characterize the structural relationship between uncertain concepts in which the vertices and edges are assigned positive and negative membership function values to feature the opposite uncertainty elevation. The dominating set is the control set of vertices in the graph structure and it occupies a critical position in graph analysis. This paper mainly contributes to extending the concept of domination in the fuzzy graph to the bipolar frameworks and obtaining the related expanded concepts of a variety of bipolar fuzzy graphs. Meanwhile, the approaches to obtain the specific dominating sets are presented. Finally, a numeral example on city data in Yunnan Province is presented to explain the computing of domination in bipolar fuzzy graph in the specific application.

A Novel Approach on Energy of λJ-dominating Single-Valued Neutrosophic Graph Structure

“…To find out more, it is suggested to study at the research papers. The following studies [23][24][25] provide some helpful information about these kinds of structures. In 2022, Bera, S., and Pal, M. [26] presented a new idea regarding domination in m-polar interval-valued FG.…”

Connectivity indices of m-polar fuzzy network model, with an application to a product manufacturing problem

“…Recently, Gong et al. ( 2021 ) studied domination of bipolar fuzzy graphs. Akram and Waseem ( 2016 ) established the concept of m -PF graphs in order to study network models with multi-polar, multi-attribute information.…”

“…In the analysis of bipolar fuzzy graphs (Akram 2011), Poulik and Ghorai (2020) introduced certain indices and produced related applications. Recently, Gong et al (2021) studied domination of bipolar fuzzy graphs. Akram and Waseem (2016) established the concept of m-PF graphs in order to study network models with multi-polar, multi-attribute information.…”

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“…In a certain period of time, devices tend to be in a disconnected state, which leads to the need to select a collection of devices that are in working state during each iteration of federated learning. For various reasons of actual needs, network connectivity has become a hot topic in the field of information technology (see Cheung and Bell [1], Yemini et al [2], Burla et al [3], Denison et al [4], Hummer et al [5], Ma et al [6], Gong et al [7], Gao et al [8,9], and Kumar et al [10]).…”