Some Properties of Double Domination in Vague Graphs with an Application

• Published in: Symmetry (Basel) Vol. 15; no. 5; p. 1003
• Main Authors: Rao, Yongsheng, Cai, Ruiqi, Talebi, Ali Asghar, Mojahedfar, Masomeh
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 29.04.2023
• Subjects: Apexes; Eigenvalues; Energy; Fuzzy sets; Graph theory; Graphs; Mathematical functions; Symmetry
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym15051003

This paper is devoted to the study of the double domination in vague graphs, and it is a contribution to the Special Issue “Advances in graph theory and Symmetry/Asymmetry” of Symmetry. Symmetry is one of the most important criteria that illustrate the structure and properties of fuzzy graphs. It has many applications in dominating sets and helps find a suitable place for construction. Vague graphs (VGs), which are a family of fuzzy graphs (FGs), are a well-organized and useful tool for capturing and resolving a range of real-world scenarios involving ambiguous data. In the graph theory, a dominating set (DS) for a graph G*=(X,E) is a subset D of the vertices X so that every vertex which is not in D is adjacent to at least one member of D. The subject of energy in graph theory is one of the most attractive topics serving a very important role in biological and chemical sciences. Hence, in this work, we express the notion of energy on a dominating vague graph (DVG) and also use the concept of energy in modeling problems related to DVGs. Moreover, we introduce a new notion of a double dominating vague graph (DDVG) and provide some examples to explain various concepts introduced. Finally, we present an application of energy on DVGs.