An improved upper bound for the Laplacian spectral radius of graphs |
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| Authors: | Mei Lu Huiqing Liu Feng Tian |
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| Institution: | aDepartment of Mathematical Sciences, Tsinghua University, Beijing 100084, China;bSchool of Mathematics and Computer Science, Hubei University, Wuhan 430062, China;cInstitute of Systems Science, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | Let G be a simple graph with n vertices, m edges. Let Δ and δ be the maximum and minimum degree of G, respectively. If each edge of G belongs to t triangles (t≥1), then we present a new upper bound for the Laplacian spectral radius of G as follows: Moreover, we give an example to illustrate that our result is, in some cases, the best. |
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| Keywords: | Graph Laplacian spectral radius Maximum and minimum degree |
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