The signless Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the smallest eigenvalue of its signless Laplacian matrix. In this paper, we determine the first to llth large...The signless Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the smallest eigenvalue of its signless Laplacian matrix. In this paper, we determine the first to llth largest signless Laplacian spectral radii in the class of bicyclic graphs with n vertices. Moreover, the unique bicyclic graph with the largest or the second largest signless Laplacian spread among the class of connected bicyclic graphs of order n is determined, respectively.展开更多
The choice of fulcrums for control of socio-economic systems represented by direc ted weighted signed graphs is a topic of current interest.This article proposes a new method for identifying nodes of impact and influe...The choice of fulcrums for control of socio-economic systems represented by direc ted weighted signed graphs is a topic of current interest.This article proposes a new method for identifying nodes of impact and influential nodes,which will provide a guaranteed positive system response over the growth model.The task is posed as an optimization problem to maximize the ratio of the norms of the accumulated increments of the growth vector and the exogenous impact vector.The algorithm is reduced to solving a quadratic programming problem with nonlinear restrictions.The selection of the most effective vertices is based on the cumulative gains of the component projections onto the solution vector.Numerical examples arc provided to illustrate the effectiveness of the proposed method.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11171273)Graduate Starting Seed Fund of Northwestern Polytechnical University(Grant No.Z2014173)
文摘The signless Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the smallest eigenvalue of its signless Laplacian matrix. In this paper, we determine the first to llth largest signless Laplacian spectral radii in the class of bicyclic graphs with n vertices. Moreover, the unique bicyclic graph with the largest or the second largest signless Laplacian spread among the class of connected bicyclic graphs of order n is determined, respectively.
基金Supported by the Natural Science Foundation of Shanghai(No11ZR1425100)the Innovation Program of Shanghai Municipal Education Commission(No11YZ241)Mathematics and Applied Mathematics by Special Fund of Shanghai(No1130IA15)
基金supported by the Russian Foundation for Basic Research (No. 17-01-00076)
文摘The choice of fulcrums for control of socio-economic systems represented by direc ted weighted signed graphs is a topic of current interest.This article proposes a new method for identifying nodes of impact and influential nodes,which will provide a guaranteed positive system response over the growth model.The task is posed as an optimization problem to maximize the ratio of the norms of the accumulated increments of the growth vector and the exogenous impact vector.The algorithm is reduced to solving a quadratic programming problem with nonlinear restrictions.The selection of the most effective vertices is based on the cumulative gains of the component projections onto the solution vector.Numerical examples arc provided to illustrate the effectiveness of the proposed method.
