Arithmetical Structures On Fan Graphs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917944458477568 |
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| author | Chhetri, Dilli Ram Behera, Namita Yadav, Raj Bhawan |
| author_facet | Chhetri, Dilli Ram Behera, Namita Yadav, Raj Bhawan |
| contents | In this paper, we study the arithmetical structures on Fan Graphs Fn. Let G be a finite and connected graph. An arithmetical structure on G is a pair (d, r) of positive integer vectors such that r is primitive (the greatest common divisor of its coefficients is 1) and (diag(d)-A)r = 0, where A represents the adjacency matrix of G. This work explores the combinatorial properties of the arithmetical structures associated with Fn. Further, we discuss the arrow-star graph, a structure derived from the fan graph, along with its properties. Additionally, we investigate the critical group linked to each such structure on Fn. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01913 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Arithmetical Structures On Fan Graphs Chhetri, Dilli Ram Behera, Namita Yadav, Raj Bhawan Combinatorics 11D72, 15B48, 11D45, 11B83, 11D68, 11C20 In this paper, we study the arithmetical structures on Fan Graphs Fn. Let G be a finite and connected graph. An arithmetical structure on G is a pair (d, r) of positive integer vectors such that r is primitive (the greatest common divisor of its coefficients is 1) and (diag(d)-A)r = 0, where A represents the adjacency matrix of G. This work explores the combinatorial properties of the arithmetical structures associated with Fn. Further, we discuss the arrow-star graph, a structure derived from the fan graph, along with its properties. Additionally, we investigate the critical group linked to each such structure on Fn. |
| title | Arithmetical Structures On Fan Graphs |
| topic | Combinatorics 11D72, 15B48, 11D45, 11B83, 11D68, 11C20 |
| url | https://arxiv.org/abs/2503.01913 |