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Internet Electronic Journal of Molecular Design - IEJMD, ISSN 1538-6414, CODEN IEJMAT
| ABSTRACT - Internet Electron. J. Mol. Des. December 2007, Volume 6, Number 12, 375-384 |
Further Results on the Largest Eigenvalues of the Distance Matrix
and Some Distance-Based Matrices of Connected (Molecular) Graphs
Bo Zhou and Nenad Trinajstić
Internet Electron. J. Mol. Des. 2007, 6, 375-384
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Abstract:
Our aim in this report was to detect the upper and lower bounds for the
largest eigenvalue of the distance matrix of a connected (molecular) graph
involving the distance sums. In addition, we also wanted to detect the
largest eigenvalues of related distance-based matrices such as the detour
matrix, the Harary matrix (the reciprocal distance matrix) and the
complementary distance matrix. The methods of graph theory and matrix
algebra are used. The upper and lower bounds for the largest eigenvalues
of distance matrix and several related distance-based matrices are
established. The bounds for the largest eigenvalues of the four types of
distance matrices of connected (molecular) graphs considered here involve
the row sums.
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