Proof of a conjecture involving the second largest D-eigenvalue and the number of triangles
Proof of a conjecture involving the second largest D-eigenvalue and the number of triangles
复制标题
DOI：
10.1016/j.laa.2015.01.034
复制
发表时间：
2015-05
影响因子：
1.1
通讯作者：
Huiqiu Lin
中科院分区：
文献类型：
--
作者：
Huiqiu Lin
设G是具有tr个三角形的n阶连通图，D是G的距离矩阵，λ1(D)≥λ2(D)≥⋯≥λn(D)是图G的D-特征值.Fajtlowicz(1998)[4]猜想λ2(D)≤tr当独立数α(G)≤2时.本文证明了这一猜想，并刻画了等式成立时的极图.
Let G be a connected graph of order n with tr triangles and D be the distance matrix of G. Let λ 1 (D)≥ λ 2 (D)≥⋯≥ λ n (D) be the D-eigenvalue of the graph G. Fajtlowicz (1998)[4] conjectured that λ 2 (D)≤ tr when the independent number α (G)≤ 2. In this paper, the conjecture is confirmed and the extremal graph when the equality holds is characterized.