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

Abstract

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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 H v a l f ( G ) ≡ ∑ e ∈ E g ( e ) m o d 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.

How to cite

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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

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  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). 

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