2025/03/01 by Chhetri, Dilli Ram, Behera, Namita, Yadav, Raj Bhawan
#11B83 #11C20 #11D45 #11D68 #11D72 #15B48 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.01913
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.