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Extremal Matching Energy of Complements of Trees

100%
Wu T., Yan W., Zhang H.
Discussiones Mathematicae Graph Theory
|
2016
|
tom 36
|
nr 3
505-521
EN
Gutman and Wagner proposed the concept of the matching energy which is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph. And they pointed out that the chemical applications of matching energy go back to the 1970s. Let T be a tree with n vertices. In this paper, we characterize the trees whose complements have the maximal, second-maximal and minimal matching energy. Furthermore, we determine the trees with edge-independence number p whose complements have the minimum matching energy for p = 1, 2, . . . , [n/2]. When we restrict our consideration to all trees with a perfect matching, we determine the trees whose complements have the second-maximal matching energy.
2
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On the energy of unit vector fields with isolated singularities

100%
Brito F. G. B., Walczak P. G.
Annales Polonici Mathematici
|
2000
|
tom 73
|
nr 3
269-274
EN
We consider the energy of a unit vector field defined on a compact Riemannian manifold M except at finitely many points. We obtain an estimate of the energy from below which appears to be sharp when M is a sphere of dimension >3. In this case, the minimum of energy is attained if and only if the vector field is totally geodesic with two singularities situated at two antipodal points (at the 'south and north pole').
3
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Harmonic conformal flows on manifolds of constant curvature

63%
Fawaz A.
Open Mathematics
|
2007
|
tom 5
|
nr 3
493-504
EN
We compute the energy of conformal flows on Riemannian manifolds and we prove that conformal flows on manifolds of constant curvature are critical if and only if they are isometric.
4
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Distinguished geodesics and jacobi fields on first order jet spaces

51%
Balan V., Voicu N.
Open Mathematics
|
2004
|
tom 2
|
nr 4
516-526
EN
In the framework of jet spaces endowed with a non-linear connection, the special curves of these spaces (h-paths, v-paths, stationary curves and geodesics) which extend the corresponding notions from Riemannian geometry are characterized. The main geometric objects and the paths are described and, in the case when the vertical metric is independent of fiber coordinates, the first two variations of energy and the extended Jacobi field equations are derived.
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