Fat Hoffman graphs with smallest eigenvalue greater than -3

TL;DR

This paper characterizes the special graphs of fat Hoffman graphs with a specific subgraph and a smallest eigenvalue greater than -3, advancing understanding of their spectral properties.

Contribution

It provides a combinatorial characterization of certain fat Hoffman graphs with eigenvalue constraints, focusing on graphs containing a specific subgraph.

Findings

Characterization of special graphs with eigenvalue > -3

Identification of subgraph structures influencing eigenvalues

Extension of Hoffman graph spectral theory

Abstract

In this paper, we give a combinatorial characterization of the special graphs of fat Hoffman graphs containing $\mathfrak{K}_{1,2}$ with smallest eigenvalue greater than -3, where $\mathfrak{K}_{1,2}$ is the Hoffman graph having one slim vertex and two fat vertices.