Geodesic
On the energy and spectral properties of the he matrix of hexagonal systems
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 47-63
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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.
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.
DOI : 10.1007/s10587-013-0003-7
Classification : 05C10, 05C30, 68R10, 81Q30
Keywords: molecular graph; hexagonal system; inner dual; He matrix; spectral radius; eigenvalue; energy of graph 
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Bhatti, Faqir M.; Das, Kinkar Ch.; Ahmed, Syed A. On the energy and spectral properties of the he matrix of hexagonal systems. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 47-63. doi: 10.1007/s10587-013-0003-7

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