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arXiv · 2503.01913

Arithmetical Structures On Fan Graphs

Dilli Ram Chhetri·Namita Behera·Raj Bhawan Yadav
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Abstract

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.

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Dilli Ram Chhetri, Namita Behera, Raj Bhawan Yadav. 2025-03-01. Arithmetical Structures On Fan Graphs. https://arxiv.org/abs/2503.01913

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