On the spectral spread of bicyclic graphs with given girth |
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Authors: | Bing Wang Ming-qing Zhai Jin-long Shu |
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Affiliation: | [1]School of Mathematical Science, Chuzhou University, Anhui, Chuzhou 239012, China [2]Department of Mathematics, East China Normal University, Shanghai 200241, China |
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Abstract: | The spectral spread of a graph is defined to be the difference between the largest and the least eigenvalue of the adjacency matrix of the graph. A graph G is said to be bicyclic, if G is connected and |E(G)| = |V (G)| + 1. Let B(n, g) be the set of bicyclic graphs on n vertices with girth g. In this paper some properties about the least eigenvalues of graphs are given, by which the unique graph with maximal spectral spread in B(n, g) is determined. |
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Keywords: | bicyclic graph least eigenvalue spectral spread |
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