无符号拉普拉斯谱半径的新上界

A New Upper Bound on the Signless Laplacian Spectral Radius of Graphs

如果一个图存在定向满足其最大出度△^+不超过最大度△的一半,则通过估计图的半边路径(semi-edge walk)的个数,得到了该图的无符号拉普拉斯谱半径的一个新上界.进而根据D.Goncalves对平面图边分解的结果,得到了平面图无符号拉普拉斯谱半径的一个新上界.

For a graph,if there exists an orientation such that the maximum outdegree△^＋ is no more than half of the maximum degree A,we obtain a new upper bound of the signless Laplacian spectral radius of the graph,by estimating the number of the semi-edge walks of the graph.Moreover,combining with the result of the edge decomposition of a planar graph by D.Goncalves,a new upper bound of the signless Laplacian spectral radius of a planar graph is presented.