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On the Spectral properties of Andrásfai Graphs

Bharani Dharan K, S Radha

Abstract

In this paper, we investigate the spectral properties of Andrásfai graphs, focusing on key parameters: the second-largest and smallest eigenvalues, the number of distinct eigenvalues, and the multiplicities of the eigenvalues 1 and -1. The results obtained reveal insights into the connectivity, the structural properties, and the spectral distinctiveness.

On the Spectral properties of Andrásfai Graphs

Abstract

In this paper, we investigate the spectral properties of Andrásfai graphs, focusing on key parameters: the second-largest and smallest eigenvalues, the number of distinct eigenvalues, and the multiplicities of the eigenvalues 1 and -1. The results obtained reveal insights into the connectivity, the structural properties, and the spectral distinctiveness.
Paper Structure (4 sections, 5 theorems, 48 equations, 1 figure)

This paper contains 4 sections, 5 theorems, 48 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main Results
  4. Conclusion

Key Result

Theorem 3.1

Let G be an Andrásfai Graph $And(k)$. Then G has $k+\lceil{\frac{k}{2}}\rceil$ distinct adjacency eigenvalues.

Figures (1)

  • Figure 1: Andrásfai Graphs for $k=3,4,5$

Theorems & Definitions (14)

  • Definition 2.1
  • Theorem 3.1
  • proof
  • Theorem 3.2
  • proof
  • Theorem 3.3
  • proof
  • Lemma 3.4
  • proof
  • Lemma 3.5
  • ...and 4 more