In this paper,we determine graphs with the largest Laplacian spectral radius among the unicyclic and the bicyclic graphs on n vertices with k pendant vertices,respectively.
边数等于点数加1的连通图称为双圈图.设B(n)表示所有n阶双圈图的集合,μ(G)和Δ(G)分别表示图G的拉普拉斯谱半径和其最大度.本文证明了对于B(n)中的两个图G1和G_2,若Δ(G_1)>Δ(G_2)且△(G_1)≥(n+5)/2,则μ(G_1)>μ(G_2).作为该...边数等于点数加1的连通图称为双圈图.设B(n)表示所有n阶双圈图的集合,μ(G)和Δ(G)分别表示图G的拉普拉斯谱半径和其最大度.本文证明了对于B(n)中的两个图G1和G_2,若Δ(G_1)>Δ(G_2)且△(G_1)≥(n+5)/2,则μ(G_1)>μ(G_2).作为该结论的应用,本文确定了B(n)中图的第五大至第八大的拉普拉斯谱半径以及相应的极图(其中前四大的拉普拉斯谱半径以及相应的极图在文献[C.X.He,J.Y.Shao,J.L.He,On the Laplacian spectral radii of bicyclicgraphs,Discrete Mathematics,2008,308:5981-5995.]中已确定).展开更多
In this paper, sharp upper bounds for the Laplacian spectral radius and the spectral radius of graphs are given, respectively. We show that some known bounds can be obtained from our bounds. For a bipartite graph G, w...In this paper, sharp upper bounds for the Laplacian spectral radius and the spectral radius of graphs are given, respectively. We show that some known bounds can be obtained from our bounds. For a bipartite graph G, we also present sharp lower bounds for the Laplacian spectral radius and the spectral radius, respectively.展开更多
Let Bn^k be the class of bipartite graphs with n vertices and k cut edges. The extremal graphs with the first and the second largest Laplacian spectral radius among all graphs in Bn^K are presented. The bounds of the ...Let Bn^k be the class of bipartite graphs with n vertices and k cut edges. The extremal graphs with the first and the second largest Laplacian spectral radius among all graphs in Bn^K are presented. The bounds of the Laplacian spectral radius of these extremal graphs are also obtained.展开更多
Let T（n,i） be the set of all trees with order n and matching number i.We determine the third to sixth trees in T（2i ＋ 1,i） and the third to fifth trees in T（n,i） for n ≥ 2i ＋ 2 with the largest Laplacian spec...Let T（n,i） be the set of all trees with order n and matching number i.We determine the third to sixth trees in T（2i ＋ 1,i） and the third to fifth trees in T（n,i） for n ≥ 2i ＋ 2 with the largest Laplacian spectral radius.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10871204)the Fundamental Research Funds for the Central Universities (Grant No.09CX04003A)
文摘In this paper,we determine graphs with the largest Laplacian spectral radius among the unicyclic and the bicyclic graphs on n vertices with k pendant vertices,respectively.
基金Supported by Shanghai Leading Academic Discipline Project(No.S30104)
文摘边数等于点数加1的连通图称为双圈图.设B(n)表示所有n阶双圈图的集合,μ(G)和Δ(G)分别表示图G的拉普拉斯谱半径和其最大度.本文证明了对于B(n)中的两个图G1和G_2,若Δ(G_1)>Δ(G_2)且△(G_1)≥(n+5)/2,则μ(G_1)>μ(G_2).作为该结论的应用,本文确定了B(n)中图的第五大至第八大的拉普拉斯谱半径以及相应的极图(其中前四大的拉普拉斯谱半径以及相应的极图在文献[C.X.He,J.Y.Shao,J.L.He,On the Laplacian spectral radii of bicyclicgraphs,Discrete Mathematics,2008,308:5981-5995.]中已确定).
文摘In this paper, sharp upper bounds for the Laplacian spectral radius and the spectral radius of graphs are given, respectively. We show that some known bounds can be obtained from our bounds. For a bipartite graph G, we also present sharp lower bounds for the Laplacian spectral radius and the spectral radius, respectively.
基金Fundamental Research Funds for the Central Universities of China(No. 11D10902,No. 11D10913)
文摘Let Bn^k be the class of bipartite graphs with n vertices and k cut edges. The extremal graphs with the first and the second largest Laplacian spectral radius among all graphs in Bn^K are presented. The bounds of the Laplacian spectral radius of these extremal graphs are also obtained.
基金Supported by the National Natural Science Foundation of China (Grant No.10871204)
文摘Let T（n,i） be the set of all trees with order n and matching number i.We determine the third to sixth trees in T（2i ＋ 1,i） and the third to fifth trees in T（n,i） for n ≥ 2i ＋ 2 with the largest Laplacian spectral radius.
