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The Complexity of Some Classes of Pyramid Graphs Created from a Gear Graph

1
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
2
Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah 41411, Saudi Arabia
3
Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El Kom 32511, Egypt
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(12), 689; https://doi.org/10.3390/sym10120689
Received: 8 November 2018 / Revised: 22 November 2018 / Accepted: 23 November 2018 / Published: 2 December 2018
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
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PDF [1615 KB, uploaded 7 December 2018]
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Abstract

The methods of measuring the complexity (spanning trees) in a finite graph, a problem related to various areas of mathematics and physics, have been inspected by many mathematicians and physicists. In this work, we defined some classes of pyramid graphs created by a gear graph then we developed the Kirchhoff’s matrix tree theorem method to produce explicit formulas for the complexity of these graphs, using linear algebra, matrix analysis techniques, and employing knowledge of Chebyshev polynomials. Finally, we gave some numerical results for the number of spanning trees of the studied graphs. View Full-Text
Keywords: complexity; Chebyshev polynomials; gear graph; pyramid graphs complexity; Chebyshev polynomials; gear graph; pyramid graphs
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Liu, J.-B.; Daoud, S.N. The Complexity of Some Classes of Pyramid Graphs Created from a Gear Graph. Symmetry 2018, 10, 689.

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