On Energy of Double Dominating Bipolar Single-Valued Neutrosophic Graph
Domination and graph energy are fundamental concepts in graph theory for addressing unpredictable phenomena, and they have attracted considerable interest from researchers. In recent developments, the concept of dominating energy has become increasingly significant in the study of graph energies. Wh...
| id |
Mohamad S.N.F.; Hasni R.; Smarandache F. |
|---|---|
| spelling |
Mohamad S.N.F.; Hasni R.; Smarandache F. 2-s2.0-105000050068 On Energy of Double Dominating Bipolar Single-Valued Neutrosophic Graph 2025 International Journal of Neutrosophic Science 26 1 10.54216/IJNS.260106 https://www.scopus.com/inward/record.uri?eid=2-s2.0-105000050068&doi=10.54216%2fIJNS.260106&partnerID=40&md5=e11710b05360249cef8a41ddb811eaa6 Domination and graph energy are fundamental concepts in graph theory for addressing unpredictable phenomena, and they have attracted considerable interest from researchers. In recent developments, the concept of dominating energy has become increasingly significant in the study of graph energies. While fuzzy graphs (FG) sometimes fall short in delivering optimal results, the neutrosophic set (NS) as well as neutrosophic graphs (NG) offer a robust alternative, effectively managing the uncertainties linked with inconsistent and indeterminate information in real-world scenarios. Most existing research on domination energy in the fuzzy environment focus solely on a single membership function. In contrast, bipolar neutrosophic models, which account for both positive and negative influences, provide a more versatile and applicable approach. This paper focuses on advancements in NG theory to address scenarios where imprecision is represented by both positive and negative membership functions. It introduces a new concept called the double dominating energy graph, relying on the currently developed bipolar single-valued neutrosophic graphs (BSVNG). The study further explores the energy of double domination within the BSVNG framework. Specifically, it develops the adjacency matrix of a dominating BSVNG, analyzes the spectrum of this matrix, and elaborates on the associated theoretical aspects using illustrative examples. Additionally, the double domination energy of BSVNG is calculated to demonstrate its applicability. At the end of this study, conclusions are drawn and avenues for future research are discussed. © 2025, American Scientific Publishing Group (ASPG). All rights reserved. American Scientific Publishing Group (ASPG) 26926148 English Article |
| author |
2-s2.0-105000050068 |
| spellingShingle |
2-s2.0-105000050068 On Energy of Double Dominating Bipolar Single-Valued Neutrosophic Graph |
| author_facet |
2-s2.0-105000050068 |
| author_sort |
2-s2.0-105000050068 |
| title |
On Energy of Double Dominating Bipolar Single-Valued Neutrosophic Graph |
| title_short |
On Energy of Double Dominating Bipolar Single-Valued Neutrosophic Graph |
| title_full |
On Energy of Double Dominating Bipolar Single-Valued Neutrosophic Graph |
| title_fullStr |
On Energy of Double Dominating Bipolar Single-Valued Neutrosophic Graph |
| title_full_unstemmed |
On Energy of Double Dominating Bipolar Single-Valued Neutrosophic Graph |
| title_sort |
On Energy of Double Dominating Bipolar Single-Valued Neutrosophic Graph |
| publishDate |
2025 |
| container_title |
International Journal of Neutrosophic Science |
| container_volume |
26 |
| container_issue |
1 |
| doi_str_mv |
10.54216/IJNS.260106 |
| url |
https://www.scopus.com/inward/record.uri?eid=2-s2.0-105000050068&doi=10.54216%2fIJNS.260106&partnerID=40&md5=e11710b05360249cef8a41ddb811eaa6 |
| description |
Domination and graph energy are fundamental concepts in graph theory for addressing unpredictable phenomena, and they have attracted considerable interest from researchers. In recent developments, the concept of dominating energy has become increasingly significant in the study of graph energies. While fuzzy graphs (FG) sometimes fall short in delivering optimal results, the neutrosophic set (NS) as well as neutrosophic graphs (NG) offer a robust alternative, effectively managing the uncertainties linked with inconsistent and indeterminate information in real-world scenarios. Most existing research on domination energy in the fuzzy environment focus solely on a single membership function. In contrast, bipolar neutrosophic models, which account for both positive and negative influences, provide a more versatile and applicable approach. This paper focuses on advancements in NG theory to address scenarios where imprecision is represented by both positive and negative membership functions. It introduces a new concept called the double dominating energy graph, relying on the currently developed bipolar single-valued neutrosophic graphs (BSVNG). The study further explores the energy of double domination within the BSVNG framework. Specifically, it develops the adjacency matrix of a dominating BSVNG, analyzes the spectrum of this matrix, and elaborates on the associated theoretical aspects using illustrative examples. Additionally, the double domination energy of BSVNG is calculated to demonstrate its applicability. At the end of this study, conclusions are drawn and avenues for future research are discussed. © 2025, American Scientific Publishing Group (ASPG). All rights reserved. |
| publisher |
American Scientific Publishing Group (ASPG) |
| issn |
26926148 |
| language |
English |
| format |
Article |
| accesstype |
|
| record_format |
scopus |
| collection |
Scopus |
| _version_ |
1828987858759712768 |