Graphs with two main and two plain eigenvalues
Sakander Hayat, Muhammad Javaid, Jack H. Koolen
TL;DR
This paper introduces new spectral concepts for graphs and characterizes those with exactly two main and two plain eigenvalues, advancing understanding of their spectral properties.
Contribution
It defines the plain eigenvalue, main-plain index, and refined spectrum, and provides characterizations for graphs with two main and two plain eigenvalues.
Findings
Defined plain eigenvalue, main-plain index, and refined spectrum.
Characterized graphs with two main and two plain eigenvalues.
Enhanced spectral analysis of specific graph classes.
Abstract
In this paper, we introduce the concepts of the plain eigenvalue, the main-plain index and the refined spectrum of graphs. We focus on the graphs with two main and two plain eigenvalues and give some characterizations of them.
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