Novel Concept of Energy in Bipolar Single-Valued Neutrosophic Graphs with Applications

Abstract

The energy of a graph is defined as the sum of the absolute values of its eigenvalues. Recently, there has been a lot of interest in graph energy research. Previous literature has suggested integrating energy, Laplacian energy, and signless Laplacian energy with single-valued neutrosophic graphs (SVNGs). This integration is used to solve problems that are characterized by indeterminate and inconsistent information. However, when the information is endowed with both positive and negative uncertainty, then bipolar single-valued neutrosophic sets (BSVNs) constitute an appropriate knowledge representation of this framework. A BSVNs is a generalized bipolar fuzzy structure that deals with positive and negative uncertainty in real-life problems with a larger domain. In contrast to the previous study, which directly used truth and indeterminate and false membership, this paper proposes integrating energy, Laplacian energy, and signless Laplacian energy with BSVNs to graph structure considering the positive and negative membership degree to greatly improve decisions in certain problems. Moreover, this paper intends to elaborate on characteristics of eigenvalues, upper and lower bound of energy, Laplacian energy, and signless Laplacian energy. We introduced the concept of a bipolar single-valued neutrosophic graph (BSVNG) for an energy graph and discussed its relevant ideas with the help of examples. Furthermore, the significance of using bipolar concepts over non-bipolar concepts is compared numerically. Finally, the application of energy, Laplacian energy, and signless Laplacian energy in BSVNG are demonstrated in selecting renewable energy sources, while optimal selection is suggested to illustrate the proposed method. This indicates the usefulness and practicality of this proposed approach in real life.

[Retracted] A Decision‐Making Framework for University Student Sports Study Psychological Healthy Evaluation with 2‐Tuple Linguistic Neutrosophic Numbers

“…e relationship between the attributes can be independent or related to each other [9][10][11][12]. (3) Attributes weight: for di erent evaluation attributes, decision-makers may have di erent preference information and assign di erent weights to di erent evaluation attributes.…”

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

“…The dominating energy in a single-valued NG was recently proposed by Mullai and Broumi [37]. Novel Concept of Energy in Bipolar Single-Valued NGs with Applications was proposed by Mohamad, S.N.F., Hasni, R., Smarandache, et al [38].…”