On split graphs with four distinct eigenvalues
Combinatorics
2014-05-15 v1
Abstract
It is a well-known fact that a graph of diameter has at least eigenvalues. Let us call a graph \emph{-extremal} if it has diameter and exactly eigenvalues. Such graphs have been intensively studied by various authors. %Much attention has been devoted to the study of graphs that are extremal with respect to this relation: \emph{i.e} have diameter and exactly distinct eigenvalues. A graph is \emph{split} if its vertex set can be partitioned into a clique and a stable set. Such a graph has diameter at most . We obtain a complete classification of the connected bidegreed -extremal split graphs. We also show how to construct certain families of non-bidegreed -extremal split graphs.
Keywords
Cite
@article{arxiv.1405.3441,
title = {On split graphs with four distinct eigenvalues},
author = {Felix Goldberg and Steve Kirkland and Anu Varghese and Ambat Vijayakumar},
journal= {arXiv preprint arXiv:1405.3441},
year = {2014}
}