### Abstract

Original language | English |
---|---|

Pages (from-to) | 231-241 |

Journal | Discrete mathematics |

Volume | 283 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 2004 |

### Fingerprint

### Keywords

- Diophantine equation
- Integral graph
- Graph spectrum
- IR-76197
- Complete r-partite graph

### Cite this

*Discrete mathematics*,

*283*(1-3), 231-241. https://doi.org/10.1016/j.disc.2004.02.011

}

*Discrete mathematics*, vol. 283, no. 1-3, pp. 231-241. https://doi.org/10.1016/j.disc.2004.02.011

**Integral complete r-partite graphs.** / Wang, Ligong; Li, Xueliang; Hoede, C.

Research output: Contribution to journal › Article › Academic

TY - JOUR

T1 - Integral complete r-partite graphs

AU - Wang, Ligong

AU - Li, Xueliang

AU - Hoede, C.

PY - 2004

Y1 - 2004

N2 - A graph is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper, we give a useful sufficient and necessary condition for complete r-partite graphs to be integral, from which we can construct infinite many new classes of such integral graphs. It is proved that the problem of finding such integral graphs is equivalent to the problem of solving some Diophantine equations. The discovery of these integral complete r-partite graphs is a new contribution to the search of such integral graphs. Finally, we propose several basic open problems for further study.

AB - A graph is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper, we give a useful sufficient and necessary condition for complete r-partite graphs to be integral, from which we can construct infinite many new classes of such integral graphs. It is proved that the problem of finding such integral graphs is equivalent to the problem of solving some Diophantine equations. The discovery of these integral complete r-partite graphs is a new contribution to the search of such integral graphs. Finally, we propose several basic open problems for further study.

KW - Diophantine equation

KW - Integral graph

KW - Graph spectrum

KW - IR-76197

KW - Complete r-partite graph

U2 - 10.1016/j.disc.2004.02.011

DO - 10.1016/j.disc.2004.02.011

M3 - Article

VL - 283

SP - 231

EP - 241

JO - Discrete mathematics

JF - Discrete mathematics

SN - 0012-365X

IS - 1-3

ER -