New concepts of vague graphs

The concept of vague graph was introduced by Ramakrishna (Int J Comput Cognit 7:51–58, 2009 ). Since the vague models give more precision, flexibility, and compatibility to the system as compared to the classical and fuzzy models, in this paper, the concept of energy of fuzzy graph is extended to th...

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Bibliographic Details
Published inInternational journal of machine learning and cybernetics Vol. 8; no. 4; pp. 1081 - 1092
Main Authors Borzooei, R. A., Rashmanlou, Hossein
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2017
Springer Nature B.V
Subjects
Artificial Intelligence
Combinatorial analysis
Complex Systems
Computational Intelligence
Control
Energy
Engineering
Fuzzy sets
Graphs
Mathematical analysis
Matrices (mathematics)
Mechatronics
Original Article
Pattern Recognition
Robotics
Systems Biology
Upper bounds
Vague graph
Vague set
Energy of vague graph
05C99
05C22
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Summary:The concept of vague graph was introduced by Ramakrishna (Int J Comput Cognit 7:51–58, 2009 ). Since the vague models give more precision, flexibility, and compatibility to the system as compared to the classical and fuzzy models, in this paper, the concept of energy of fuzzy graph is extended to the energy of a vague graph . It has many applications in physics , chemistry , computer science , and other branches of mathematics. We define adjacency matrix , degree matrix , laplacian matrix , spectrum , and energy of a vague graph in terms of their adjacency matrix. The spectrum of a vague graph appears in physics statistical problems, and combinatorial optimization problems in mathematics. Also, the lower and upper bounds for the energy of a vague graph are also derived. Finally, we give some applications of energy in vague graph and other sciences.
ISSN:1868-8071
1868-808X
DOI:10.1007/s13042-015-0475-x