McKay trees
Avraham Aizenbud, Inna Entova-Aizenbud

TL;DR
This paper classifies all undirected trees that are McKay graphs of finite groups, providing a concise characterization and exploring partial classifications of forest-shaped McKay graphs with some non-trivial examples.
Contribution
It offers a complete classification of tree-shaped McKay graphs and partial results for forest-shaped graphs, linking graph structures to group representations.
Findings
All undirected trees that are McKay graphs are classified.
A partial classification of forest-shaped McKay graphs is provided.
Examples of non-trivial forest McKay graphs are constructed.
Abstract
Given a finite group and its representation , the corresponding McKay graph is a graph whose vertices are the irreducible representations of ; the number of edges between two vertices of is . The collection of all McKay graphs for a given group encodes, in a sense, its character table. Such graphs were also used by McKay to provide a bijection between the finite subgroups of and the affine Dynkin diagrams of types , the bijection given by considering the appropriate McKay graphs. In this paper, we classify all (undirected) trees which are McKay graphs of finite groups and describe the corresponding pairs ; this classification turns out to be very concise. Moreover, we give a partial classification of McKay graphs which are forests, and construct some…
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Taxonomy
TopicsFinite Group Theory Research · Synthesis and Reactivity of Heterocycles · Metal complexes synthesis and properties
