University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 1 Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry) 2010 04 01 Wiener Way to Dimensionality 5 15 5150 10.22052/ijmc.2010.5150 EN O. ORI Via Casilina, Italy F. CATALDO Via Casilina, Italy D. VUKIČEVIĆ University of Split, Croatia A GRAOVAC The R. Bošković Institute”, Croatia Journal Article 2014 04 22 This note introduces a new general conjecture correlating the dimensionality dT of an infinite lattice with N nodes to the asymptotic value of its Wiener Index W(N). In the limit of large N the general asymptotic behavior W(N)≈Ns is proposed, where the exponent s and dT are related by the conjectured formula s=2+1/dT allowing a new definition of dimensionality dW=(s-2)-1. Being related to the topological Wiener index, dW is therefore called Wiener dimensionality. Successful applications of this method to various infinite lattices (like graphene, nanocones, Sierpinski fractal triangle and carpet) testify the validity of the conjecture for infinite lattices. https://ijmc.kashanu.ac.ir/article_5150_6de0a526852fe0f62c2951d4172451bd.pdf