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

Edgar G. DuCasse; Michael L. Gargano; Louis V. Quintas

Discussiones Mathematicae Graph Theory (2010)

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

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topEdgar 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] 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] J.A. Gallian, A dynamic survey of graph labeling, Electronic J. Combin. 14 (2007) #DS6. Zbl0953.05067
- [3] J.A. Gallian, Contemporary Abstract Algebra, 6th Edition (Houghton-Mifflin, Boston, Massachusetts, 2006). Zbl0972.00001
- [4] D.B. West, Introduction to Graph Theory, 2nd Edition (Prentice Hall, Upper Saddle River, New Jersey, 2001).

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