Arithmetical Structures On Fan Graphs
Combinatorics
2025-03-05 v1
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.
Keywords
Cite
@article{arxiv.2503.01913,
title = {Arithmetical Structures On Fan Graphs},
author = {Dilli Ram Chhetri and Namita Behera and Raj Bhawan Yadav},
journal= {arXiv preprint arXiv:2503.01913},
year = {2025}
}
Comments
23 pages, 4 figures