Let T denote a tree with the diameter d(d≥2) and order n. Let Pd,r,n-d-1 denote the tree obtained by identifying the rth vertex of path Pd+1 and the center of star K1,n-d-1, where r = r(d) is the integer part about d...Let T denote a tree with the diameter d(d≥2) and order n. Let Pd,r,n-d-1 denote the tree obtained by identifying the rth vertex of path Pd+1 and the center of star K1,n-d-1, where r = r(d) is the integer part about d+2/2. Then p(T) ≤p(Pd,r,n-d-1),and equality holds if and only if T≌ Pd,r,n-d-1展开更多
Let ：T2k＋1 be the set of trees on 2k＋ 1 vertices with nearly perfect matchings, and let S2k＋2 be the set of trees on 2k ＋ 2 vertices with perfect matchings. The largest Laplacian spectral radii of trees in ：T2k...Let ：T2k＋1 be the set of trees on 2k＋ 1 vertices with nearly perfect matchings, and let S2k＋2 be the set of trees on 2k ＋ 2 vertices with perfect matchings. The largest Laplacian spectral radii of trees in ：T2k＋l and S2k＋2 and the corresponding trees were given by Guo （2003）. In this paper, the authors determine the second to the sixth largest Laplacian spectral radii among all trees in T2k＋1 and give the corresponding trees.展开更多
文摘Let T denote a tree with the diameter d(d≥2) and order n. Let Pd,r,n-d-1 denote the tree obtained by identifying the rth vertex of path Pd+1 and the center of star K1,n-d-1, where r = r(d) is the integer part about d+2/2. Then p(T) ≤p(Pd,r,n-d-1),and equality holds if and only if T≌ Pd,r,n-d-1
基金supported by the National Natural Science Foundation of China under Grant No. 10331020.
文摘Let ：T2k＋1 be the set of trees on 2k＋ 1 vertices with nearly perfect matchings, and let S2k＋2 be the set of trees on 2k ＋ 2 vertices with perfect matchings. The largest Laplacian spectral radii of trees in ：T2k＋l and S2k＋2 and the corresponding trees were given by Guo （2003）. In this paper, the authors determine the second to the sixth largest Laplacian spectral radii among all trees in T2k＋1 and give the corresponding trees.
