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.

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Presenters: Hang Do & Timothy Singer

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May 15th, 12:15 PM May 15th, 1:30 PM

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.

 

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