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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.18073 |
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| _version_ | 1866910210049703936 |
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| author | Li, Nero Ziyu Hu, Frank Xin Britz, Thomas |
| author_facet | Li, Nero Ziyu Hu, Frank Xin Britz, Thomas |
| contents | Iterated Graph Systems (IGS) transplant ideas from fractal geometry into graph theory. Building on this framework, we extend Edge IGS from the primitive to the reducible setting. Within this broader context, we formulate rigorous definitions of multifractality and multiscale-freeness for fractal graphs, and we establish conditions that are equivalent to the occurrence of these two phenomena. We further determine the corresponding fractal and degree spectra, proving that both are finite and discrete. These results complete the foundational theory of Edge IGS by filling the gap left by the primitive case studied in [1, 2]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18073 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reducible Iterated Graph Systems: multiscale-freeness and multifractals Li, Nero Ziyu Hu, Frank Xin Britz, Thomas Combinatorics Mathematical Physics Iterated Graph Systems (IGS) transplant ideas from fractal geometry into graph theory. Building on this framework, we extend Edge IGS from the primitive to the reducible setting. Within this broader context, we formulate rigorous definitions of multifractality and multiscale-freeness for fractal graphs, and we establish conditions that are equivalent to the occurrence of these two phenomena. We further determine the corresponding fractal and degree spectra, proving that both are finite and discrete. These results complete the foundational theory of Edge IGS by filling the gap left by the primitive case studied in [1, 2]. |
| title | Reducible Iterated Graph Systems: multiscale-freeness and multifractals |
| topic | Combinatorics Mathematical Physics |
| url | https://arxiv.org/abs/2506.18073 |