The substring reversal graph $R_n$ is the graph whose vertices are the permutations $S_n$, and where two permutations are adjacent if one is obtained from a substring reversal of the other. We determine the spectral gap of $R_n$, and show that its spectrum contains many integer values. Further we consider a family of graphs that generalize the prefix reversal (or pancake flipping) graph, and show that every graph in this family has adjacency spectral gap equal to one.
@article{10_37236_6894,
author = {Fan Chung and Josh Tobin},
title = {The spectral gap of graphs arising from substring reversals},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {3},
doi = {10.37236/6894},
zbl = {1368.05093},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6894/}
}
TY - JOUR
AU - Fan Chung
AU - Josh Tobin
TI - The spectral gap of graphs arising from substring reversals
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/6894/
DO - 10.37236/6894
ID - 10_37236_6894
ER -
%0 Journal Article
%A Fan Chung
%A Josh Tobin
%T The spectral gap of graphs arising from substring reversals
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/6894/
%R 10.37236/6894
%F 10_37236_6894
Fan Chung; Josh Tobin. The spectral gap of graphs arising from substring reversals. The electronic journal of combinatorics, Tome 24 (2017) no. 3. doi: 10.37236/6894
