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New concepts of vague graphs

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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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Acknowledgments

The authors are thankful to all the reviewers, the Associate Editor, and the Editor-in-Chief of the journal for their important suggestions to improve the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Shahid Beheshti University, Tehran, Iran

    R. A. Borzooei

  2. Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran

    Hossein Rashmanlou

Authors
  1. R. A. Borzooei
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  2. Hossein Rashmanlou
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Correspondence to Hossein Rashmanlou.

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Borzooei, R.A., Rashmanlou, H. New concepts of vague graphs. Int. J. Mach. Learn. & Cyber. 8, 1081–1092 (2017). https://doi.org/10.1007/s13042-015-0475-x

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  • DOI: https://doi.org/10.1007/s13042-015-0475-x

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