Upper bounds for the Zagreb indices and the spectral radius of series‐parallel graphs | Zendy

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Upper bounds for the Zagreb indices and the spectral radius of series‐parallel graphs

Author(s) -

Zhou Bo

Publication year - 2006

Publication title -

international journal of quantum chemistry

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.484

H-Index - 105

eISSN - 1097-461X

pISSN - 0020-7608

DOI - 10.1002/qua.21223

Subject(s) - spectral radius , adjacency matrix , combinatorics , eigenvalues and eigenvectors , mathematics , series (stratigraphy) , upper and lower bounds , radius , graph , adjacency list , graph energy , physics , quantum mechanics , computer science , mathematical analysis , graph power , line graph , paleontology , computer security , biology

The first Zagreb index M 1 is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index M 2 is equal to the sum of the products of the degrees of pairs of adjacent vertices of the respective graph. The spectral radius of a graph is the largest eigenvalue of its adjacency matrix. The Zagreb indices and the spectral radius are all useful molecular structure descriptors. We provide upper bounds for the Zagreb indices M 1 and M 2 and the spectral radius of series‐parallel graphs, in terms of the number of vertices and the number of edges, and determine the graphs for which the bounds are attained. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

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