This paper presents a new theoretical approach for the description of multidimensional objects for which 3D and 4D are particular cases. The approach is based on a curved space which is associated to each object. This curved space is characterised by Riemannian tensors from which invariant quantities are defined. A descriptor or index is constructed from those invariants for which statistical a...

The incidence energy I E (G) of a graph G, defined as the sum of the singular values of the incidence matrix of a graph G, is a much studied quantity with well known applications in chemical physics. The Laplacian-energy-like invariant of G is defined as the sum of square roots of the Laplacian eigenvalues. In this paper, we obtain the closed-form formulae expressing the incidence energy and th...

In this paper, at rst we describe a graph representing all the weak-order extensions of a partially ordered set and an algorithm generating them. Then we present a graph representing all of the minimal weak-order extensions of a partially ordered set, and implying a generation algorithm. Finally, we prove that the number of weak-order extensions of a partially ordered set is a comparability inv...

Let p,s 2 ð0,1 with s4p, let m,n 2 N with 1omon, and define V={1,y,n}. Let ER(n,p) denote the random graph model on V where each edge is independently included in the graph with probability p. Let kðn,p,m,sÞ denote the random graph model on V where each edge among the m vertices {1,y,m} is independently included in the graph with probability s and all other edges are independently included with...

Abstract We show that every graded ideal of a Leavitt path algebra is isomorphic to algebra. It known I the graph, as generalised hedgehog which defined based on certain sets vertices uniquely determined by . However, this isomorphism may not be graded. replacing short ‘spines’ graph with possibly fewer, but then necessarily longer spines, we obtain (which call porcupine graph) whose Our proof ...

In 2010, Vukičević introduced an new graph invariant, the inverse sum indeg index of a graph, which has been studied due to its wide range applications. Let Bnd be class bipartite graphs order n and diameter d. this paper, we mainly characterize in with maximal index. Bipartite largest, second-largest, smallest indexes are also completely characterized.

The families of one-dimensional maps have been the object of many studies since [Sharkovsky, 1964], for instance in [Sharkovsky et al., 1997] or in [de Melo & van Strien, 1993], whose authors also studied this subject, we have two large surveys of the enormous effort made in the last decades in this field of work. We adopt the usual definitions as for instance symbolic dynamics or topological e...

It is shown that bright cluster dwarf ellipticals follow a relation between metallicity and apparent flattening. Rounder dwarfs tend to be more metal-rich. The evidence is based on colour as well as spectroscopic line-strength data from the literature. The large scatter of dEs around the mean metallicity-luminosity relation, usually ascribed to large observational errors, turns out to be an ell...

Finite directed graphs with relations define finite-dimensional algebras given as factor algebras of the corresponding path algebras. In joint work with T. Holm, we studied invariants of an associated generalized Cartan matrix for certain types of algebras where the Cartan invariants basically count nonzero paths; the main motivation for this came from the context of derived module categories a...