The k-th spectral moment M_k(G) of the adjacency matrix of a graph G represents the number of closed walks of length k in G. We study here the partial order ≼ of graphs, defined by G ≼ H if M_k(G) ≤ M_k(H) for all k ≥ 0, and are interested in the question when is ≼ a linear order within a specified set of graphs? Our main result is that ≼ is a linear order on each set of starlike trees with constant number of vertices. Recall that a connected graph G is a starlike tree if it has a vertex u such that the components of G − u are paths, called the branches of G. It turns out that the ≼ ordering of starlike trees with constant number of vertices coincides with the shortlex order of sorted sequence of their branch lengths.

的ķ个频谱力矩中号_ķ（ģ的曲线图的邻接矩阵的）ģ代表长度的封闭的阶层的数量ķ在ģ。在这里，我们研究图的偏序≼，由下式定义ģ ≼ ħ如果中号_ķ（ģ）≤中号_ķ（ħ）的所有ķ时是≼指定的一组内的线性顺序≥0，和感兴趣的问题图？我们的主要结果是，≼是每组具有恒定顶点数的星形树的线性阶数。回想一下连通图G如果它的顶点u使得G − u的分量是路径，则称为星形树，称为G的分支。事实证明，具有恒定顶点数的星形树的≼顺序与其分支长度的排序序列的shortlex顺序重合。