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On the Szeged and the Laplacian Szeged spectrum of a graph |
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| Authors: | Gholam Hossein Fath-Tabar Ali Reza Ashrafi |
| Institution: | a Department of Mathematics, Faculty of Science, University of Kashan, Kashan 87317-51167, Iran b Faculty of Civil Engineering, University of Zagreb, Ka?i?eva 26, 10000 Zagreb, Croatia c School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran |
| Abstract: | For a given graph G its Szeged weighting is defined by w(e)=nu(e)nv(e), where e=uv is an edge of G,nu(e) is the number of vertices of G closer to u than to v, and nv(e) is defined analogously. The adjacency matrix of a graph weighted in this way is called its Szeged matrix. In this paper we determine the spectra of Szeged matrices and their Laplacians for several families of graphs. We also present sharp upper and lower bounds on the eigenvalues of Szeged matrices of graphs. |
| Keywords: | 05C35 05C12 05A20 05C05 |
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