Two graphs $G$ and $H$ are called $\mathbb{R}$-cospectral if $A(G)+yJ$ and $A(H)+yJ$ (where $A(G)$, $A(H)$ are the adjacency matrices of $G$ and $H$, respectively, $J$ is the all-one matrix) have the same spectrum for all $y\in\mathbb{R}$. In this note, we give a necessary condition for having $\mathbb{R}$-cospectral graphs. Further, we provide a sufficient condition ensuring only irrational orthogonal similarity between certain cospectral graphs. Some concrete examples are also supplied to exemplify the main results.
@article{10_37236_6002,
author = {Fenjin Liu and Wei Wang},
title = {A note on {non-\(\mathbb{R}\)-cospectral} graphs},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {1},
doi = {10.37236/6002},
zbl = {1358.05175},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6002/}
}
TY - JOUR
AU - Fenjin Liu
AU - Wei Wang
TI - A note on non-\(\mathbb{R}\)-cospectral graphs
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/6002/
DO - 10.37236/6002
ID - 10_37236_6002
ER -
%0 Journal Article
%A Fenjin Liu
%A Wei Wang
%T A note on non-\(\mathbb{R}\)-cospectral graphs
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/6002/
%R 10.37236/6002
%F 10_37236_6002
Fenjin Liu; Wei Wang. A note on non-\(\mathbb{R}\)-cospectral graphs. The electronic journal of combinatorics, Tome 24 (2017) no. 1. doi: 10.37236/6002
