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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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