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International Journal of Machine Learning and Cybernetics
Published in: International Journal of Machine Learning and Cybernetics 4/2017

31-12-2015 | Original Article

New concepts of vague graphs

Authors: R. A. Borzooei, Hossein Rashmanlou

Published in: International Journal of Machine Learning and Cybernetics | Issue 4/2017

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Abstract

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.
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Metadata
Title
New concepts of vague graphs
Authors
R. A. Borzooei
Hossein Rashmanlou
Publication date
31-12-2015
Publisher
Springer Berlin Heidelberg
Published in
International Journal of Machine Learning and Cybernetics / Issue 4/2017
Print ISSN: 1868-8071
Electronic ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-015-0475-x

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