On the energy and spectral properties of the He matrix of hexagonal systems |
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Authors: | Faqir M. Bhatti Kinkar Ch. Das Syed A. Ahmed |
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Affiliation: | 13. Sector U, DHA, Lahore University of Management Sciences, Lahore, 54792, Pakistan 23. Sungkyunkwan University, Suwon, 440-746, Republic of Korea
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Abstract: | The He matrix, put forward by He and He in 1989, is designed as a means for uniquely representing the structure of a hexagonal system (= benzenoid graph). Observing that the He matrix is just the adjacency matrix of a pertinently weighted inner dual of the respective hexagonal system, we establish a number of its spectral properties. Afterwards, we discuss the number of eigenvalues equal to zero of the He matrix of a hexagonal system. Moreover, we obtain a relation between the number of triangles and the eigenvalues of the He matrix of a hexagonal system. Finally, we present an upper bound on the He energy of hexagonal systems. |
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