TY - JOUR

T1 - On graphs with three eigenvalues

AU - Muzychuk, Mikhail

AU - Klin, Mikhail

N1 - Funding Information:
* Corresponding author.E-mail: [email protected]. ’ Partially supported by the Ministry of Science of Israel and by the grant No I-0333-263.06/93 from the G.I.F., the G erman-Israeli Foundation for Scientific Research and Development. 2 Partially supported by the Israeli Ministry of Absorption, by the grant No I-0333-263.06/93 from the G.I.F., the German -Israeli Foundation for Scientific Research and Development, and by the Department of Mathematics and Computing Science, The University of the South Pacific, Suva, Fiji Islands.

PY - 1998/7/28

Y1 - 1998/7/28

N2 - We consider undirected non-regular connected graphs without loops and multiple edges (other than complete bipartite graphs) which have exactly three distinct eigenvalues (such graphs are called non-standard graphs). The interest in these graphs is motivated by the questions posed by W. Haemers during the 15th British Combinatorial Conference (Stirling, July 1995); the main question concerned the existence of such graphs. A brief review of two papers by Bridges and Mena (1979, 1981) is followed by the presentation of our new results and examples concerning, in particular, the construction of some non-standard graphs. This answers problems posed by Haemers. Other open problems are suggested and discussed in the final section.

AB - We consider undirected non-regular connected graphs without loops and multiple edges (other than complete bipartite graphs) which have exactly three distinct eigenvalues (such graphs are called non-standard graphs). The interest in these graphs is motivated by the questions posed by W. Haemers during the 15th British Combinatorial Conference (Stirling, July 1995); the main question concerned the existence of such graphs. A brief review of two papers by Bridges and Mena (1979, 1981) is followed by the presentation of our new results and examples concerning, in particular, the construction of some non-standard graphs. This answers problems posed by Haemers. Other open problems are suggested and discussed in the final section.

UR - http://www.scopus.com/inward/record.url?scp=0042284276&partnerID=8YFLogxK

U2 - 10.1016/S0012-365X(98)00084-3

DO - 10.1016/S0012-365X(98)00084-3

M3 - Article

AN - SCOPUS:0042284276

SN - 0012-365X

VL - 189

SP - 191

EP - 207

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -