The Largest Eigenvalue Calculating Scheme of Catacondensed Benzenoids in Environment Engineering

Fu Qin Zhan; Ou Fu Qiao

doi:10.4028/www.scientific.net/AMM.340.407

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 340The Largest Eigenvalue Calculating Scheme of...

The Largest Eigenvalue Calculating Scheme of Catacondensed Benzenoids in Environment Engineering

Abstract:

The characteristic polynomial of a graph is defined as, where is the identity matrix and is the adjacency matrix of. In this work, we define the coalescence of two graphs with respect to edges, and show for the graph and in Fig. 2, which are obtained by coalescence of bipartite graphs around the six-vertex cycle. Moreover, we give ordering relations with respect to the largest Eigen value in the class of cat condensed hexagonal systems. These results generalize some known results on extremely hexagonal chains.

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Periodical:

Applied Mechanics and Materials (Volume 340)

Pages:

407-410

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.340.407

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Online since:

July 2013

Authors:

Fu Qin Zhan, Ou Fu Qiao

Keywords:

Cat Condensed Systems, Characteristic Polynomials, Eigen Value, Hexagonal Systems

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References

[1] Gutman I., Cyvin S. J.: Introduction to the Theory of Benzenoid Hydrocarbons. Berlin, Springer 13, 14-21 (1989).

Google Scholar

[2] Bondy J. A., Murty U. S. R.: Graph Theory with Applications. Amsterdam: North-Holland 16, 22-28 (1976).

Google Scholar

[3] Gutman I., Polansky O. E.: Mathematical Concepts in Organic Chemistry. Berlin, Springer-Verlag 19, 15-19 (1986).

Google Scholar

[4] Gutman I.: Extremely hexagonal chains. J. Math. Chem 12, 197-210 (1993).

Google Scholar

[5] Zhang L. Z., Tian F.: Extremely hexagonal chains concerning largest eigenvalue. Sciences in China (Series A) 44, 1089-1097 (2001).

DOI: 10.1007/bf02877425

Google Scholar

[6] Schwenk A.: Computing the characteristic polynomial of a graph. Lecture Notes in Mathematics 406, 153-172 (1974).

Google Scholar

[7] Gutman I. (Ed): Advance in the Theory of Benzenoid Hydrocarbons, Topics in Current Chemistry 163, Springer, Berlin(1992).

Google Scholar

[8] Juan Rada: Energy ordering of catacondensed hexagonal systems. Discrete Applied Mathematic 145, 437-443(2005).

DOI: 10.1016/j.dam.2004.03.007

Google Scholar

[9] Zhang L. Z., Tian F.: Extremal cat condensed benzenoids. J. Math. Chem. 34(12), 111-122 (2003).

Google Scholar