# Value sets of graphs edge-weighted with elements of a finite abelian group

• Volume: 30, Issue: 1, page 5-15
• ISSN: 2083-5892

top

## Abstract

top
Given a graph G = (V,E) of order n and a finite abelian group H = (H,+) of order n, a bijection f of V onto H is called a vertex H-labeling of G. Let g(e) ≡ (f(u)+f(v)) mod H for each edge e = u,v in E induce an edge H-labeling of G. Then, the sum $Hva{l}_{f}\left(G\right)\equiv {\sum }_{e\in E}g\left(e\right)modH$ is called the H-value of G relative to f and the set HvalS(G) of all H-values of G over all possible vertex H-labelings is called the H-value set of G. Theorems determining HvalS(G) for given H and G are obtained.

## How to cite

top

Edgar G. DuCasse, Michael L. Gargano, and Louis V. Quintas. "Value sets of graphs edge-weighted with elements of a finite abelian group." Discussiones Mathematicae Graph Theory 30.1 (2010): 5-15. <http://eudml.org/doc/271012>.

@article{EdgarG2010,
abstract = {Given a graph G = (V,E) of order n and a finite abelian group H = (H,+) of order n, a bijection f of V onto H is called a vertex H-labeling of G. Let g(e) ≡ (f(u)+f(v)) mod H for each edge e = u,v in E induce an edge H-labeling of G. Then, the sum $Hval_f(G) ≡ ∑_\{e ∈ E\} g(e) mod H$ is called the H-value of G relative to f and the set HvalS(G) of all H-values of G over all possible vertex H-labelings is called the H-value set of G. Theorems determining HvalS(G) for given H and G are obtained.},
author = {Edgar G. DuCasse, Michael L. Gargano, Louis V. Quintas},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {graph labeling; edge labeling; vertex labeling; abelian group; Abelian group},
language = {eng},
number = {1},
pages = {5-15},
title = {Value sets of graphs edge-weighted with elements of a finite abelian group},
url = {http://eudml.org/doc/271012},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Edgar G. DuCasse
AU - Michael L. Gargano
AU - Louis V. Quintas
TI - Value sets of graphs edge-weighted with elements of a finite abelian group
JO - Discussiones Mathematicae Graph Theory
PY - 2010
VL - 30
IS - 1
SP - 5
EP - 15
AB - Given a graph G = (V,E) of order n and a finite abelian group H = (H,+) of order n, a bijection f of V onto H is called a vertex H-labeling of G. Let g(e) ≡ (f(u)+f(v)) mod H for each edge e = u,v in E induce an edge H-labeling of G. Then, the sum $Hval_f(G) ≡ ∑_{e ∈ E} g(e) mod H$ is called the H-value of G relative to f and the set HvalS(G) of all H-values of G over all possible vertex H-labelings is called the H-value set of G. Theorems determining HvalS(G) for given H and G are obtained.
LA - eng
KW - graph labeling; edge labeling; vertex labeling; abelian group; Abelian group
UR - http://eudml.org/doc/271012
ER -

## References

top
1. [1] E.G. DuCasse, M.L. Gargano, and L.V. Quintas, The edge-weight sums of a graph mod n (to have been presented at Thirty-Ninth Southeastern International Conference on Combinatorics, Graph Theory, and Computing, Florida Atlantic University, Boca Raton, Florida, March 3-7, 2008 by Michael L. Gargano, who could not do so due to illness).
2. [2] J.A. Gallian, A dynamic survey of graph labeling, Electronic J. Combin. 14 (2007) #DS6. Zbl0953.05067
3. [3] J.A. Gallian, Contemporary Abstract Algebra, 6th Edition (Houghton-Mifflin, Boston, Massachusetts, 2006). Zbl0972.00001
4. [4] D.B. West, Introduction to Graph Theory, 2nd Edition (Prentice Hall, Upper Saddle River, New Jersey, 2001).

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.