The spectral radii of a graph and its line graph |
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Authors: | Lingsheng Shi |
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Affiliation: | Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China |
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Abstract: | The spectral radius of a (directed) graph is the largest eigenvalue of adjacency matrix of the (directed) graph. We give the relation on the characteristic polynomials of a directed graph and its line graph, and obtain sharp bounds on the spectral radius of directed graphs. We also give the relation on the spectral radii of a graph and its line graph. As a consequence, the spectral radius of a connected graph does not exceed that of its line graph except that the graph is a path. |
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Keywords: | 05C50 15A42 |
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