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The hyper-Wiener index is a kind of extension of the Wiener index, used for predicting physicochemical properties of organic compounds. The hyper-Wiener index W W(G) is defined as WW(G) =1/2∑_(u,v)∈V(G)(d_G(u, v) + d_G~2(u,v)) with the summation going over all pairs of vertices in G, d_G(u,v) denotes the distance of the two vertices u and v in the graph G. In this paper,we study the minimum hyper-Wiener indices among all the unicyclic graph with n vertices and diameter d, and characterize the corresponding extremal graphs. 相似文献
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Generalized Petersen graphs are commonly used interconnection networks,and wide diameter is an important parameter to measure fault-tolerance and efficiency of parallel pro- cessing computer networks.In this paper,we show that the diameter and 3-wide diameter of generalized Petersen graph P (m,a) are both O( m 2a ),where a ≥ 3. 相似文献
106.
Sanja Marušić 《Applicable analysis》2013,92(3-4):379-401
Using the homogenization theory, we derive the nonlinear Reynolds equation governing the process of lubrication of a slipper bearing with rapidly rotating shaft. We prove that this nonliner lubrication law is an approximation of the full Navier-Stokes equations in a thin cylinder with periodic roughness. The analyticity of the nonlinear function giving the relation between the velocity and the pressure drop is proved. The first term in its Taylor's expansion is the classical linear Reynolds law. Boundary layer correctors are computed. 相似文献
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Russell Merris 《Linear and Multilinear Algebra》2013,61(2-3):275-285
If G is a graph on n vertices, its Laplacian matrix L(G) = D(G) - A(G) is the difference of the diagonal matrix of vertex degrees and the adjacency matrix. The main purpose of this note is to continue the study of the positive definite, doubly stochastic graph matrix (In + L(G))?1= ω(G) = (wij). If, for example, w(G) = min wij, then w(G)≥0 with equality if and only if G is disconnected and w(G) ≤ l/(n + 1) with equality if and only if G = Kn. If i¦j, then wii ≥2wij, with equality if and only if the ith vertex has degree n - 1. In a sense made precise in the note, max w,, identifies most remote vertices of G. Relations between these new graph invariants and the algebraic connectivity emerge naturally from the fact that the second largest eigenvalue of ω(G) is 1/(1 + a(G)). 相似文献
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Xianya Geng 《Linear and Multilinear Algebra》2013,61(1):41-56
A tricyclic graph is a connected graph with n vertices and n + 2 edges. In this article, we determine graphs with the largest spectral radius among the n-vertex tricyclic graphs with given diameter d. 相似文献