this note introduces a new general conjecture correlating the dimensionality dt of an infinitelattice with n nodes to the asymptotic value of its wiener index w(n). in the limit of large nthe general asymptotic behavior w(n)≈ns is proposed, where the exponent s and dt are relatedby the conjectured formula s=2+1/dt allowing a new definition of dimensionality dw=(s-2)-1.being related to the topol...

in this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable taylor and weight function approximation. the method is based on weerakoon-fernando method [s. weerakoon, g.i. fernando, a variant of newton's method with third-order convergence, appl. math. lett. 17 (2000) 87-93]. the method is optimal, as it needs three evaluations per ite...

A new type of decomposition of graphs – the operator decomposition connected with the classical notion of homogeneous set (or module) is introduced. The properties of this decomposition are described. Using this decomposition we prove the following. Let P and Q be two hereditary graph classes such that P is closed with respect to the operation of join and Q is closed with respect to the operati...

A modified k-deck of a graph G is obtained by removing k edges of G in all possible ways, and adding k (not necessarily new) edges in all possible ways. Krasikov and Roditty asked if it was possible to construct the usual k-edge deck of a graph from its modified k-deck. Earlier I solved this problem for the case when k = 1. In this paper, the problem is completely solved for arbitrary k. The pr...

A modified k-deck of a graph is obtained by removing k edges in all possible ways and adding k (not necessarily new) edges in all possible ways. Krasikov and Roditty used these decks to give an independent proof of Müller’s result on the edge reconstructibility of graphs. They asked if a k-edge deck could be constructed from its modified k-deck. In this paper, we solve the problem when k = 1. W...

A graph is said to be reconstructible if it is determined up to isomorphism from the collection of all its one-vertex deleted unlabeled subgraphs. The Reconstruction Conjecture (RC) asserts that all graphs on at least three vertices are reconstructible. In this paper, we prove that all triangle-free graphs G with connectivity two such that diam(G) = 2 or diam(G) = diam(G) = 3 are reconstructibl...

In this paper we de2ne 2ve families of simple graphs {fi,f2,f^,t^ and F=5) such that the reconstruction conjecture is true if reconstruction is proved for either the families $[,$2 & % or the families F=3;F=4 and F=5. These families are quite restrictive in that each has diameter two or three. Then we prove that families F=1;F=2;F=3;F=4 and F=5 are recognizable by proving that graphs of diamete...

We show that the three body Calogero model with inverse square potentials can be interpreted as a maximally superintegrable and multiseparable system in Euclidean three-space. As such it is a special case of a family of systems involving one arbitrary function of one