No Threshold graphs are cospectral

J. Lazzarin; O. F. Márquez; F. Tura

No Threshold graphs are cospectral

Combinatorics 2018-06-20 v1

Authors: J. Lazzarin , O. F. Márquez , F. Tura

Abstract

A threshold graph G on n vertices is defined by binary sequence of length n. In this paper we present an explicit formula for computing the characteristic polynomial of a threshold graph from its binary sequence. Applications include obtaining a formula for the determinant of adjacency matrix of a threshold graph and showing that no two nonisomorphic threshold graphs are cospectral.

Keywords

graph polynomials graph theory spectral graph theory

Cite

@article{arxiv.1806.07358,
  title  = {No Threshold graphs are cospectral},
  author = {J. Lazzarin and O. F. Márquez and F. Tura},
  journal= {arXiv preprint arXiv:1806.07358},
  year   = {2018}
}