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