Arithmetical Structures on Wheel Graphs
Bibhas Adhikari, Namita Behera, Dilli Ram Chhetri, and Raj Bhawan, Yadav
TL;DR
This paper investigates arithmetical structures on wheel graphs, exploring the properties and characteristics of such structures within this specific class of graphs.
Contribution
It provides a detailed analysis of arithmetical structures on wheel graphs, a previously less-studied class, expanding understanding of their combinatorial and algebraic properties.
Findings
Characterization of arithmetical structures on wheel graphs
Enumeration formulas for these structures
Insights into their algebraic and combinatorial properties
Abstract
An arithmetical structure on a finite and connected graph G is a pair (d, r) of positive integer vectors such that r is primitive (the gcd of its entries is 1) and (diag(d) - A)r = 0, where A is the adjacency matrix of G. In this article, we investigate arithmetical structures on the wheel graphs.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Cellular Automata and Applications · Advanced Graph Theory Research