#### Title

The Game of Graph Nim

#### Date

5-29-2014 10:15 AM

#### End Time

29-5-2014 10:35 AM

#### Location

Math & Nursing Building (MNB) 104

#### Department

Mathematics

#### Session Chair

Michael Ward

#### Session Title

Mathematics Senior Project Presentations

#### Faculty Sponsor(s)

Breeann Flesch

#### Presentation Type

Presentation

#### Abstract

Nim is a well-known two player impartial combinatorial game. Various versions of playing Nim on graphs have been investigated. I will introduce a new version of Nim called Graph Nim. Given a graph with n vertices and edges connected to these vertices, players take turns to remove edges until there are no more edges left. Players have to choose a vertex and remove at least one edge connected to the chosen vertex. The player that removes the last edge or edges wins the game. I will give some preliminary results of winning and losing positions of Graph Nim, compare the game of Graph Nim with other impartial combinatorial games, and discuss open problems.

#### Recommended Citation

Pradhan, Akaanchya, "The Game of Graph Nim" (2014). *Academic Excellence Showcase Schedule*. 295.

http://digitalcommons.wou.edu/aes_event/2014/all/295

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The Game of Graph Nim

Math & Nursing Building (MNB) 104

Nim is a well-known two player impartial combinatorial game. Various versions of playing Nim on graphs have been investigated. I will introduce a new version of Nim called Graph Nim. Given a graph with n vertices and edges connected to these vertices, players take turns to remove edges until there are no more edges left. Players have to choose a vertex and remove at least one edge connected to the chosen vertex. The player that removes the last edge or edges wins the game. I will give some preliminary results of winning and losing positions of Graph Nim, compare the game of Graph Nim with other impartial combinatorial games, and discuss open problems.