{
  "id": "1209.2188",
  "version": "v1",
  "published": "2012-09-11T00:50:05.000Z",
  "updated": "2012-09-11T00:50:05.000Z",
  "title": "On the spectral moment of trees with given degree sequences",
  "authors": [
    "Li Shuchao",
    "Song Yibing"
  ],
  "comment": "9 pages; 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $A(G)$ be the adjacency matrix of graph $G$ with eigenvalues $\\lambda_1(G), \\lambda_2(G),..., \\lambda_n(G)$ in non-increasing order. The number $S_k(G):=\\sum_{i=1}^{n}\\lambda_i^{k}(G)\\, (k=0, 1,..., n-1)$ is called the $k$th spectral moment of $G$. Let $S(G) = (S_0(G), S_1(G),..., S_{n-1}(G))$ be the sequence of spectral moments of $G.$ For two graphs $G_1, G_2$, we have $G_1\\prec_{s}G_2$ if for some $k \\in \\{1,2,3,...,n-1\\}$, we have $S_i(G_1) = S_i(G_2)\\, ,\\, i = 0, 1,..., k-1$ and $S_k(G_1)<S_k(G_2).$ In this paper, the last $n$-vertex tree with a given degree sequence in an $S$-order is determined. Consequently, we also obtain the last trees in an $S$-order in the sets of all trees of order $n$ with the largest degree, the leaves number, the independence number and the matching number, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-11T00:50:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "degree sequence",
      "th spectral moment",
      "adjacency matrix",
      "vertex tree",
      "largest degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.2188S"
    }
  }
}