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2012 | 32 | 3 | 557-567
Tytuł artykułu

Generalized graph cordiality

Treść / Zawartość
Warianty tytułu
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
Wydawca
Rocznik
Tom
32
Numer
3
Strony
557-567
Opis fizyczny
Daty
wydano
2012
otrzymano
2011-03-30
poprawiono
2011-09-30
zaakceptowano
2011-09-30
Twórcy
  • Department of Mathematics, University of Illinois, Urbana, IL, 61801
  • 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1626
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