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

• Autorzy: Edgar G. DuCasse , Michael L. Gargano , Louis V. Quintas
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

graph labeling; edge labeling; vertex labeling; abelian group

Kategorie tematyczne

• 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
• 05C22: Signed and weighted graphs
• 05C78: Graph labelling (graceful graphs, bandwidth, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2010
• Tom: 30
• Numer: 1
• Strony: 5-15

Daty

wydano

2010

otrzymano

2008-05-23

poprawiono

2009-01-05

zaakceptowano

2009-01-05

Twórcy

autor

Edgar G. DuCasse

• Mathematics Department, Pace University, One Pace Plaza, New York, NY 10038, USA

autor

Michael L. Gargano

• Mathematics and Computer Science Departments, Pace University, One Pace Plaza, New York, NY 10038, USA

autor

Louis V. Quintas

• Mathematics Department, Pace University, One Pace Plaza, New York, NY 10038, USA

Bibliografia

• [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.
• [3] J.A. Gallian, Contemporary Abstract Algebra, 6th Edition (Houghton-Mifflin, Boston, Massachusetts, 2006).
• [4] D.B. West, Introduction to Graph Theory, 2nd Edition (Prentice Hall, Upper Saddle River, New Jersey, 2001).

Identyfikatory

DOI

10.7151/dmgt.1472