TY - JOUR
T1 - Biregular graphs with three eigenvalues
AU - Cheng, Xi Ming
AU - Gavrilyuk, Alexander L.
AU - Greaves, Gary R.W.
AU - Koolen, Jack H.
N1 - Funding Information:
J.H.K. is partially supported by the ‘100 talents’ program of the Chinese Academy of Sciences, and by the National Natural Science Foundation of China (No. 11471009 ).
Funding Information:
Part of the work was done while A.L.G. was visiting Tohoku University as a JSPS Postdoctoral Fellow. His work (e.g., Theorem 7.3 ) was also partially supported by the Russian Science Foundation (grant 14-11-00061 ).
Funding Information:
G.R.W.G. was supported by JSPS KAKENHI; grant number: 2603903 .
Publisher Copyright:
© 2016 Elsevier Ltd.
PY - 2016/8/1
Y1 - 2016/8/1
N2 - We consider nonregular graphs having precisely three distinct eigenvalues. The focus is mainly on the case of graphs having two distinct valencies and our results include constructions of new examples, structure theorems, valency constraints, and a classification of certain special families of such graphs. We also present a new example of a graph with three valencies and three eigenvalues of which there are currently only finitely many known examples.
AB - We consider nonregular graphs having precisely three distinct eigenvalues. The focus is mainly on the case of graphs having two distinct valencies and our results include constructions of new examples, structure theorems, valency constraints, and a classification of certain special families of such graphs. We also present a new example of a graph with three valencies and three eigenvalues of which there are currently only finitely many known examples.
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U2 - 10.1016/j.ejc.2016.03.004
DO - 10.1016/j.ejc.2016.03.004
M3 - Article
AN - SCOPUS:84962757895
VL - 56
SP - 57
EP - 80
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
SN - 0195-6698
ER -