Cospectral Graphs With Least Eigenvalue at Least -2
Publications de l'Institut Mathématique, _N_S_78 (2005) no. 92, p. 51
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We study the phenomenon of cospectrality in generalized line
graphs and in exceptional graphs. We survey old results from today's
point of view and obtain some new results partly by the use of
computer. Among other things, we show that a connected generalized line
graph $L(H)$ has an exceptional cospectral mate only if its root graph
$H$, assuming it is itself connected, has at most 9 vertices. The paper
contains a description of a table of sets of cospectral graphs with
least eigenvalue at least $-2$ and at most 8 vertices together with
some comments and theoretical explanations of the phenomena suggested
by the table.
Classification :
05C50
Dragoš Cvetković; Mirko Lepović. Cospectral Graphs With Least Eigenvalue at Least -2. Publications de l'Institut Mathématique, _N_S_78 (2005) no. 92, p. 51 . http://geodesic.mathdoc.fr/item/PIM_2005_N_S_78_92_a2/
@article{PIM_2005_N_S_78_92_a2,
author = {Drago\v{s} Cvetkovi\'c and Mirko Lepovi\'c},
title = {Cospectral {Graphs} {With} {Least} {Eigenvalue} at {Least} -2},
journal = {Publications de l'Institut Math\'ematique},
pages = {51 },
year = {2005},
volume = {_N_S_78},
number = {92},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_2005_N_S_78_92_a2/}
}