Publication Date:
2013-01-01
Description:
The Laplacian spectra are the eigenvalues of Laplacian matrixL(G)=D(G)-A(G), whereD(G)andA(G)are the diagonal matrix of vertex degrees and the adjacency matrix of a graphG, respectively, and the spectral radius of a graphGis the largest eigenvalue ofA(G). The spectra of the graph and corresponding eigenvalues are closely linked to the molecular stability and related chemical properties. In quantum chemistry, spectral radius of a graph is the maximum energy level of molecules. Therefore, good upper bounds for the spectral radius are conducive to evaluate the energy of molecules. In this paper, we first give several sharp upper bounds on the adjacency spectral radius in terms of some invariants of graphs, such as the vertex degree, the average 2-degree, and the number of the triangles. Then, we give some numerical examples which indicate that the results are better than the mentioned upper bounds in some sense. Finally, an upper bound of the Nordhaus-Gaddum type is obtained for the sum of Laplacian spectral radius of a connected graph and its complement. Moreover, some examples are applied to illustrate that our result is valuable.
Print ISSN:
2356-6140
Electronic ISSN:
1537-744X
Topics:
Natural Sciences in General
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