Energy of Bipolar Fuzzy Graphs

Akram, Muhammad; Sarwar, Musavarah; Dudek, Wiesław A.

doi:10.1007/978-981-15-8756-6_8

Cited by 4 publications

(3 citation statements)

References 10 publications

(12 reference statements)

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“…The concept of energy of Pythagorean FGs with applications was recently introduced by Muhammad Akram and Sumera Naz [34]. Moreover, they presented the concept of Bipolar FG Energy and Energy of double dominating bipolar FGs [35,36]. Many scholars have integrated the study of energy graphs, dominating sets, and NSs since the development of the NS.…”

Section: Introductionmentioning

confidence: 99%

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

Bathusha,

Raj

2024

Neutrosophic syst. appl.

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The concept of dominance is one of the most important ideas in graph theory for handling random events, and it has drawn the interest from many scholars. Research related to graph energy has garnered a lot focus recently. The application of single-valued neutrosophic graphs (SVNGs) for energy, Laplacian energy, and dominating energy has been recommended by previous studies. In this research, we apply the concepts of single-valued neutrosophic sets (SVNS) to graph structures (GSs) and investigate some intriguing features of single-valued neutrosophic graph structures (SVNGS). Moreover, the notions of λJ-dominating energy GS in an SVNGS environment are analyzed in this study. More specifically, illustrative examples are used to develop the adjacency matrix of a λJ-dominating SVNGS, as well as the spectrum of the adjacency matrix and their related theory. Further, the SVNGS λJ-dominating energy is determined. We go over various characteristics and constraints for the energy of SVNGS with λJ-dominating. Further, we introduce the idea of isomorphic and identical λJ-dominating SVNGS energy, which has been studied using relevant examples, and some of its established properties are presented.

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Section: Introductionmentioning

confidence: 99%

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

Bathusha,

Raj

2024

Neutrosophic syst. appl.

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“…This is a fascinating topic that has piqued the interest of academics all across the world. The concept of energy has been applied to many graphs such as bipolar fuzzy graphs was established by Akram M, Sarwar M, Dudek WA (2) , whereas the energy https://www.indjst.org/ of m-polar fuzzy digraphs and the laplacian energy of interval valued fuzzy graphs (3) was also established. The author expanded the idea of adjacency energy to include pebbling graphs (4) in 2021.…”

Section: Introductionmentioning

confidence: 99%

Minimum Degree Energy of Graphs and Pebbling Graphs

Srinivasan,

Shanmugavel

2024

IJST

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Objectives: The minimum degree energy concept is applied to pebbling graphs. This study establishes a connection between the minimum degree energy of graphs and the minimum degree energy of pebbling graphs by applying the lowest degree energy of pebbling notion to twenty standard graphs. Methods: The minimum degree energy of pebbling graph with the matrix whose was calculated using . The characteristic polynomial of the minimum degree, is must be found from the matrix. Next, the eigen values of the matrix were calculated using and the sum of all the eigen values gives the minimum degree energy. The lower and upper bounds for the minimum degree energy of graphs are established along with the algorithm for computing the minimum degree energy of graphs. Findings: The lower and upper bounds were found for the minimum degree energy of pebbling graphs. For twenty standard graphs and pebbling graphs, the minimum degree energy values were calculated, and their relation was tabulated. Novelty: Pebbling graphs were subjected to the minimal energy idea and a relationship was found between the minimum energy of pebbling graphs and the minimum energy of graphs in general. Keywords: Energy, Minimum degree energy, Grotzsch graph, Pebbling graph, Data mining

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“…If membership grade of an element is [−1, 0) which tells that its marginal pleases the implicit counter property. The idea of the symbolization of bipolar fuzzy graphs (BFGs) along with the matrices in FGs, regular and irregular BFGs, hyper BFGs and antipodal BFGs along with their various applications, properties and significance was explained by Akram et al [8][9][10][11][12][13][14]. Mohanta et al gave a study of m-polar neutrosophic graph with applications [15].…”

Section: Introductionmentioning

confidence: 99%

Applications of maximum matching by using bipolar fuzzy incidence graphs

Rehman,

Rashid,

Hussain

2023

PLoS ONE

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The extension of bipolar fuzzy graph is bipolar fuzzy incidence graph (BFIG) which gives the information regarding the effect of vertices on the edges. In this paper, the concept of matching in bipartite BFIG and also for BFIG is introduced. Some results and theorems of fuzzy graphs are also extended in BFIGs. The number of operations in BFIGs such as augmenting paths, matching principal numbers, relation between these principal numbers and maximum matching principal numbers are being investigated which are helpful in the selection of maximum most allied applicants for the job and also to get the maximum outcome with minimum loss (due to any controversial issues among the employees of a company). Some characteristics of maximum matching principal numbers in BFIG are explained which are helpful for solving the vertex and incidence pair fuzzy maximization problems. Lastly, obtained maximum matching principal numbers by using the matching concept to prove its applicability and effectiveness for the applications in bipartite BFIG and also for the BFIG.

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Energy of Bipolar Fuzzy Graphs

Cited by 4 publications

References 10 publications

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

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

Minimum Degree Energy of Graphs and Pebbling Graphs

Applications of maximum matching by using bipolar fuzzy incidence graphs

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