Graovac and Pisanski [On the Wiener index of a graph, J. Math. Chem. 8 (1991) 53 – 62] applied an algebraic approach to generalize the Wiener index by symmetry group of the molecular graph under consideration. In this paper, exact formulas for this graph invariant under some graph operations are presented.

We investigate the property of the Wu invariant metric on a certain class of psuedoconvex domains. We show that the Wu invariant Hermitian metric, which in general behaves as nicely as the Kobayashi metric under holomorphic mappings, enjoys the complex hyperbolic curvature property in such cases. Namely, the Wu invariant metric is Kähler and has constant negative holomorphic curvature in a neig...

*,+ ' /. # 0,12. 0 ( # 3%& ) 45 76 . ) 6 8' 9% : 45 <; "='>0@?A &BC &%&' "$DE # & + .: "$6 #F "$6 #F 4$ : # ' # G% . # @"5 . ' H. . %I F"$ J' %& # "5 @ & -.K & "56 # L M N 12 < <O N & + /. # % 9' I. & BC !9P2 "5 . N & @ %& "$ N 8 )@ 9 . 4=0 ?A Q'I. 6 R ) 4=' 8"$#:.J . S &BC '9' 7 D . 4$) .T'

Recently Ohtsuki Oh2], motivated by the notion of nite type knot invariants, introduced the notion of nite type invariants for oriented, integral ho-mology 3-spheres (ZHS for short). In the present paper we propose another definition of nite type invariants of Z HS and give equivalent reformulations of our notion. We show that our invariants form a ltered commutative algebra and are of nite typ...

Résumé. Les avancées technologiques récentes ont permis d’acquérir dans de nombreux domaines des corpus de graphes. Une problématique en plein essor consiste à classer ces données complexes pour établir des typologies. Différentes approches développées en fouille de données sont présentées dans cet article: la visualisation de graphes dans une perspective exploratoire, la caractérisation des gr...

We prove a spectral theorem for bimodules in the context of graph C∗-algebras. A bimodule over a suitable abelian algebra is determined by its spectrum (i.e., its groupoid partial order) iff it is generated by the Cuntz– Krieger partial isometries which it contains iff it is invariant under the gauge automorphisms. We study 1-cocycles on the Cuntz–Krieger groupoid associated with a graph C∗-alg...

Registration is a fundamental but critical task in point cloud processing, which usually depends on finding element correspondence from two clouds. However, the of reliable relies establishing robust and discriminative description elements correct matching corresponding elements. In this letter, we develop coarse-to-fine registration strategy, utilizes rotation-invariant features new weighted g...

We study a family of stable curves defined combinatorially from a trivalent graph. Most of our results are related to the conjecture of Green which relates the Clifford index of a smooth curve, an important intrinsic invariant measuring the “specialness” of the geometry of the curve, to the “resolution Clifford index,” a projective invariant defined from the canonical embedding. Thus we study t...