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On the energy and spectral properties of the he matrix of hexagonal systems

Faqir M. Bhatti, Kinkar Ch. Das, Syed A. Ahmed (2013)

Czechoslovak Mathematical Journal

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...

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