### Abstract

A fundamental idea and realization of networks arises in a variety of areas of science and engineering. Their theoretical underpinnings stem from graph theory where numerous fundamental concepts being formulated and solved there have become of immediate interest at the applied side. In this study, our focus is on the weighted maximum clique problem, a highly challenging problem in graph theory. The essence of the problem is to find the nodes with the maximum total of weights in a graph where an edge connects every pair of nodes, meaning every node connects to every other node. We propose an algorithm to find all the weighted cliques as well as the weighted maximum clique in order of size using the framework of DNA computing.

Original language | English |
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Pages (from-to) | 1561-1570 |

Number of pages | 10 |

Journal | Simulation Modelling Practice and Theory |

Volume | 16 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2008 Nov |

### Keywords

- DNA oligonucleotide
- Graph theory
- Weighted clique
- Weighted graph

### ASJC Scopus subject areas

- Hardware and Architecture
- Software
- Modelling and Simulation

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## Cite this

*Simulation Modelling Practice and Theory*,

*16*(10), 1561-1570. https://doi.org/10.1016/j.simpat.2007.11.003