The minimum length in a graph G between two vertices is defined to be the distance between the two vertices and is denoted by d$\left(a,b\right)$. The farthest vertex distance from a vertex 'a' is known as the eccentricity e(a) of the vertex 'a'. Enumerating the vertex eccentricities in an increasing order is defined as the eccentricity sequence or eccentric sequence of the graph G [11]. The eccentric sequence of some graphs is computed in this paper.
Starting from the g-natural Riemannian metric G on the tangent bundle TM of a
Riemannian manifold (M,g), we construct a family of the Golden Riemannian
structures ? on the tangent bundle (TM,G). Then we investigate the
integrability of such Golden Riemannian structures on the tangent bundle TM
and show that there is a direct correlation between the locally decomposable
property of (TM,?,G) and the locally flatness of manifold (M,g).
Abstract
We associate a flow
$\phi $
with a solution of the vortex equations on a closed oriented Riemannian 2-manifold
$(M,g)$
of negative Euler characteristic and investigate its properties. We show that
$\phi $
always admits a dominated splitting and identify special cases in which
$\phi $
is Anosov. In particular, starting from holomorphic differentials of fractional degree, we produce novel examples of Anosov flows on suitable roots of the unit tangent bundle of
$(M,g)$
.
A Tangent Bundle Theory for Visual Curve Completion
