#### Submission Title

#### Faculty Sponsor(s)

Chuck Dunn & Jennifer Nordstrom

#### Location

Jereld R. Nicholson Library

#### Subject Area

Mathematics

#### Description

We introduce a new graph labeling and derive a game on graphs called the 1-relaxed modular edge-sum labeling game. Given a graph G and a natural number n, we define a labeling by assigning to each edge a number from {1,..., n} and assign a corresponding label for each vertex *u* by the sum of the labels of the edges incident to *u*, computing this sum modulo *n*. Similar to the chromatic number, we define L(G) for a graph G as the smallest *n* such that G has a proper labeling. We provide bounds for L(G) for various classes of graphs. Motivated by competitive graph coloring, we define a game on using modular edge-sum labeling and determine the chromatic game number for various classes of graphs. We will emphasize some characteristics that distinguish this labeling from traditional vertex coloring.

#### Recommended Citation

Do, Hang; Singer, Timothy; and Moran, Brent, "1-Relaxed Edge-Sum Labeling Game" (2015). *Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement.* Event. Submission 38.

https://digitalcommons.linfield.edu/symposium/2015/all/38

1-Relaxed Edge-Sum Labeling Game

Jereld R. Nicholson Library

We introduce a new graph labeling and derive a game on graphs called the 1-relaxed modular edge-sum labeling game. Given a graph G and a natural number n, we define a labeling by assigning to each edge a number from {1,..., n} and assign a corresponding label for each vertex *u* by the sum of the labels of the edges incident to *u*, computing this sum modulo *n*. Similar to the chromatic number, we define L(G) for a graph G as the smallest *n* such that G has a proper labeling. We provide bounds for L(G) for various classes of graphs. Motivated by competitive graph coloring, we define a game on using modular edge-sum labeling and determine the chromatic game number for various classes of graphs. We will emphasize some characteristics that distinguish this labeling from traditional vertex coloring.

## Comments

Presenters: Hang Do & Timothy Singer