q-Analogs of distance matrices of 3-hypertrees
q-Analogs of distance matrices of 3-hypertrees
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DOI：
10.1016/j.laa.2009.04.020
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发表时间：
2009-09
影响因子：
1.1
通讯作者：
S. Sivasubramanian
中科院分区：
文献类型：
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作者：
S. Sivasubramanian
我们考虑3-一致超图中树的距离矩阵（我们称之为3-超树）。给出了3-超树T的距离矩阵的几个q-类似的逆矩阵的计算公式。一些结果是类似的结果Bapat等人。图。我们给出了3-超树T的距离矩阵的行列式只依赖于T的顶点数n的结果的另一种证明。此外，当我们固定顶点的顺序并适当地分配符号时，我们给出了3-超树的一些（斜对称）距离矩阵的主子矩阵的普法夫等式。Graham，霍夫曼和Hosoya的一个结果将图的距离矩阵的行列式与它的两连通块的行列式联系起来.当图的块为满足一定条件的固定连通图H时，给出了它的距离矩阵的求逆公式。这个结果推广了Graham和Lovasz的一个结果。当G的每个块是固定图G时，我们还给出了关于G的距离矩阵的逆矩阵的元素之和及其类似矩阵的一些推论。
We consider the distance matrix of trees in 3-uniform hypergraphs (which we call 3-hypertrees). We give a formula for the inverse of a few q-analogs of distance matrices of 3-hypertrees T. Some results are analogs of results by Bapat et al. for graphs. We give an alternate proof of the result that the determinant of the distance matrix of a 3-hypertree T depends only on n, the number of vertices of T. Further, we give a Pfaffian identity for a principal submatrix of some (skew-symmetrized) distance matrices of 3-hypertrees when we fix an ordering of the vertices and assign signs appropriately. A result of Graham, Hoffman and Hosoya relates the determinant of the distance matrix of a graph and the determinants of its two-connected blocks. When the graph has as blocks a fixed connected graph H which satisfy some conditions, we give a formula for the inverse of its distance matrix. This result generalises a result of Graham and Lovasz. When each block of G is a fixed graph G, we also give some corollaries about the sum of the entries of the inverse of the distance matrix of G and some of its analogs.