#### Presentation Title

Domination of Hypercubes

#### Location

IB 1020

#### Start Date

19-3-2016 10:15 AM

#### End Date

19-3-2016 10:30 AM

#### Abstract

Hypercubes are a family of graphs defined by using all possible 0-1 sequences of length n as vertices. In modern computing, hypercubes play an important role. This is because any input of an algorithm, as a 0-1 sequence, can be embedded into a hypercube. The same is true for any computer program. More recently, the hypercube has been used in designing the architectures of parallel computing. In this presentation we will define hypercubes and domination sets formally, talk about some of the practical applications of domination sets on hypercubes, and then establish upper and lower bounds on the number of vertices in the domination set of hypercubes.

#### Department

Mathematics

#### Faculty Advisor

Roger Yu

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Domination of Hypercubes

IB 1020

Hypercubes are a family of graphs defined by using all possible 0-1 sequences of length n as vertices. In modern computing, hypercubes play an important role. This is because any input of an algorithm, as a 0-1 sequence, can be embedded into a hypercube. The same is true for any computer program. More recently, the hypercube has been used in designing the architectures of parallel computing. In this presentation we will define hypercubes and domination sets formally, talk about some of the practical applications of domination sets on hypercubes, and then establish upper and lower bounds on the number of vertices in the domination set of hypercubes.