TY - JOUR
ID - 5150
TI - Wiener Way to Dimensionality
JO - Iranian Journal of Mathematical Chemistry
JA - IJMC
LA - en
SN - 2228-6489
AU - ORI, O.
AU - CATALDO, F.
AU - VUKIČEVIĆ, D.
AU - GRAOVAC, A
AD - Via Casilina, Italy
AD - University of Split, Croatia
AD - The R. Bošković Institute”, Croatia
Y1 - 2010
PY - 2010
VL - 1
IS - Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry)
SP - 5
EP - 15
KW - Wiener dimensionality
KW - Sierpinski fractals
KW - Asymptotic Wiener index
DO - 10.22052/ijmc.2010.5150
N2 - 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.
UR - https://ijmc.kashanu.ac.ir/article_5150.html
L1 - https://ijmc.kashanu.ac.ir/article_5150_6de0a526852fe0f62c2951d4172451bd.pdf
ER -