184 research outputs found
On the positive and negative inertia of weighted graphs
The number of the positive, negative and zero eigenvalues in the spectrum of
the (edge)-weighted graph are called positive inertia index, negative
inertia index and nullity of the weighted graph , and denoted by ,
, , respectively. In this paper, the positive and negative
inertia index of weighted trees, weighted unicyclic graphs and weighted
bicyclic graphs are discussed, the methods of calculating them are obtained.Comment: 12. arXiv admin note: text overlap with arXiv:1107.0400 by other
author
On the spectral moments of trees with a given bipartition
For two given positive integers and with , we denote
\mathscr{T}_n^{p, q}={T: T is a tree of order with a -bipartition}. For a graph with vertices, let be its
adjacency matrix with eigenvalues in non-increasing order. The number
is called the th
spectral moment of . Let be the
sequence of spectral moments of . For two graphs and , one has
if for some , and holds. In this paper, the last four
trees, in the -order, among
are characterized.Comment: 11 pages, 7 figure
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