Work

Communicability exponent of the Sierpiński gasket graph

Year: 2026

Type: article

Abstract: Within the “temporal wake” program (Notes 1–6) a differential communicability exponentDc was introduced as a characteristic of the scale flow of graphs. In Note 6 thisquantity was computed exactly for a regular hierarchical graph and turned out to be −2.In the present work the Sierpiński gasket graph SGn — a self-similar fractal graph builtby the classical recursive scheme — is investigated. Two geometric blocks and a blockobservable Nn(β) are rigorously defined. It is shown that the number of walks of fixedlength between the blocks stabilises as n grows, which implies the existence of a finitelimit Mn(β) → C(β) > 0 for the unnormalised inter-block sum. T

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.21899164

Author: Gromov, Alexey

Language: English

Topic: Graph theory and applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7202295396

FWCI:

Cites:

Cited by:

Related to: 10