13,419 research outputs found
The Laplacian Eigenvalues and Invariants of Graphs
In this paper, we investigate some relations between the invariants
(including vertex and edge connectivity and forwarding indices) of a graph and
its Laplacian eigenvalues. In addition, we present a sufficient condition for
the existence of Hamiltonicity in a graph involving its Laplacian eigenvalues.Comment: 10 pages,Filomat, 201
The geometric mean is a Bernstein function
In the paper, the authors establish, by using Cauchy integral formula in the
theory of complex functions, an integral representation for the geometric mean
of positive numbers. From this integral representation, the geometric mean
is proved to be a Bernstein function and a new proof of the well known AG
inequality is provided.Comment: 10 page
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