TY - JOUR
A2 - Wang, Y.
A2 - Liu, H.-L.
AU - Wang, Tianfei
AU - Jia, Liping
AU - Sun, Feng
PY - 2013
DA - 2013/06/05
TI - Bounds of the Spectral Radius and the Nordhaus-Gaddum Type of the Graphs
SP - 472956
VL - 2013
AB - The Laplacian spectra are the eigenvalues of Laplacian matrix L(G)=D(G)-A(G), where D(G) and A(G) are the diagonal matrix of vertex degrees and the adjacency matrix of a graph G, respectively, and the spectral radius of a graph G is the largest eigenvalue of A(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.
SN - 2356-6140
UR - https://doi.org/10.1155/2013/472956
DO - 10.1155/2013/472956
JF - The Scientific World Journal
PB - Hindawi Publishing Corporation
KW -
ER -