A mixed extension of a graph $G$ is a graph $H$ obtained from $G$ by replacing each vertex of $G$ by a clique or a coclique, whilst two vertices in $H$ corresponding to distinct vertices $x$ and $y$ of $G$ are adjacent whenever $x$ and $y$ are adjacent in $G$. If $G$ is the path $P_3$, then $H$ has at most three adjacency eigenvalues unequal to $0$ and $-1$. Recently, the first author classified the graphs with the mentioned eigenvalue property. Using this classification we investigate mixed extension of $P_3$ on being determined by the adjacency spectrum. We present several cospectral families, and with the help of a computer we find all graphs on at most 25 vertices that are cospectral with a mixed extension of $P_3$.
@article{10_37236_8284,
author = {Willem H. Haemers and Sezer Sorgun and Hatice Topcu},
title = {On the spectral characterization of mixed extensions of {\(P_3\)}},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {3},
doi = {10.37236/8284},
zbl = {1417.05120},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8284/}
}
TY - JOUR
AU - Willem H. Haemers
AU - Sezer Sorgun
AU - Hatice Topcu
TI - On the spectral characterization of mixed extensions of \(P_3\)
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/8284/
DO - 10.37236/8284
ID - 10_37236_8284
ER -
%0 Journal Article
%A Willem H. Haemers
%A Sezer Sorgun
%A Hatice Topcu
%T On the spectral characterization of mixed extensions of \(P_3\)
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/8284/
%R 10.37236/8284
%F 10_37236_8284
Willem H. Haemers; Sezer Sorgun; Hatice Topcu. On the spectral characterization of mixed extensions of \(P_3\). The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8284
