Generalized graph cordiality

• Autorzy: Oliver Pechenik , Jennifer Wise
• Języki publikacji: EN

Abstrakty

EN

Hovey introduced A-cordial labelings in [4] as a simultaneous generalization of cordial and harmonious labelings. If A is an abelian group, then a labeling f: V(G) → A of the vertices of some graph G induces an edge-labeling on G; the edge uv receives the label f(u) + f(v). A graph G is A-cordial if there is a vertex-labeling such that (1) the vertex label classes differ in size by at most one and (2) the induced edge label classes differ in size by at most one.
Research on A-cordiality has focused on the case where A is cyclic. In this paper, we investigate V₄-cordiality of many families of graphs, namely complete bipartite graphs, paths, cycles, ladders, prisms, and hypercubes. We find that all complete bipartite graphs are V₄-cordial except K_{m,n} where m,n ≡ 2(mod 4). All paths are V₄-cordial except P₄ and P₅. All cycles are V₄-cordial except C₄, C₅, and Cₖ, where k ≡ 2(mod 4). All ladders P₂ ☐ Pₖ are V₄-cordial except C₄. All prisms are V₄-cordial except P₂ ☐ Cₖ, where k ≡ 2(mod 4). All hypercubes are V₄-cordial, except C₄.
Finally, we introduce a generalization of A-cordiality involving digraphs and quasigroups, and we show that there are infinitely many Q-cordial digraphs for every quasigroup Q.

Słowa kluczowe

EN

graph labeling; cordial graph; A-cordial; quasigroup

Kategorie tematyczne

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

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2012
• Tom: 32
• Numer: 3
• Strony: 557-567

Daty

wydano

2012

otrzymano

2011-03-30

poprawiono

2011-09-30

zaakceptowano

2011-09-30

Twórcy

autor

Oliver Pechenik

• Department of Mathematics, University of Illinois, Urbana, IL, 61801

autor

Jennifer Wise

• Department of Mathematics, University of Illinois, Urbana, IL, 61801

Bibliografia

• [1] I. Cahit, Cordial graphs: a weaker version of graceful and harmonious graphs, Ars Combin. 23 (1987) 201-207.
• [2] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 18 (2011).
• [3] R.L. Graham and N.J.A. Sloane, On additive bases and harmonious graphs, SIAM J. Algebraic Discrete Methods 1 (1980) 382-404, doi: 10.1137/0601045.
• [4] M. Hovey, A-cordial graphs, Discrete Math. 93 (1991) 183-194, doi: 10.1016/0012-365X(91)90254-Y.
• [5] G. McAlexander, Undergraduate thesis, (Mary Baldwin College, c.2007).
• [6] A. Riskin, ℤ²₂-cordiality of complete and complete bipartite graphs, (http://arxiv.org/abs/0709.0290v1), September 2007.

Identyfikatory

DOI

10.7151/dmgt.1626