WIENER WAY TO DIMENSIONALITY

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ORI OTTORINO; CATALDO FRANCO; VUKICEVIC DAMIR; GRAOVAC ANTE

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Journal: Iranian Journal of Mathematical Chemistry Year:2010 | Volume:1 | Issue:2 Page(s): 5-15

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Information Journal Paper

Title

WIENER WAY TO DIMENSIONALITY

Author(s)

ORI OTTORINO | CATALDO FRANCO | VUKICEVIC DAMIR | GRAOVAC ANTE | Issue Writer Certificate

Keywords

WIENER DIMENSIONALITYQ3

SIERPINSKI FRACTALSQ3

ASYMPTOTIC WIENER INDEXQ3

Abstract

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.

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APA: Copy

ORI, OTTORINO, CATALDO, FRANCO, VUKICEVIC, DAMIR, & GRAOVAC, ANTE. (2010). WIENER WAY TO DIMENSIONALITY. IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY, 1(2), 5-15. SID. https://sid.ir/paper/205614/en

Vancouver: Copy

ORI OTTORINO, CATALDO FRANCO, VUKICEVIC DAMIR, GRAOVAC ANTE. WIENER WAY TO DIMENSIONALITY. IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY[Internet]. 2010;1(2):5-15. Available from: https://sid.ir/paper/205614/en

IEEE: Copy

OTTORINO ORI, FRANCO CATALDO, DAMIR VUKICEVIC, and ANTE GRAOVAC, “WIENER WAY TO DIMENSIONALITY,” IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY, vol. 1, no. 2, pp. 5–15, 2010, [Online]. Available: https://sid.ir/paper/205614/en

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