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2008 | 28 | 3 | 431-439
Tytuł artykułu

Product rosy labeling of graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we describe a natural extension of the well-known ρ-labeling of graphs (also known as rosy labeling). The labeling, called product rosy labeling, labels vertices with elements of products of additive groups. We illustrate the usefulness of this labeling by presenting a recursive construction of infinite families of trees decomposing complete graphs.
Słowa kluczowe
Wydawca
Rocznik
Tom
28
Numer
3
Strony
431-439
Opis fizyczny
Daty
wydano
2008
otrzymano
2007-04-18
poprawiono
2008-03-27
zaakceptowano
2008-05-09
Twórcy
  • Department of Mathematics and Statistics, University of Minnesota Duluth, 1117 University Dr., Duluth, MN 55812, USA
Bibliografia
  • [1] R.E.L. Aldred and B.D. McKay, Graceful and harmonious labellings of trees, Bull. Inst. Combin. Appl. 23 (1998) 69-72.
  • [2] P. Eldergill, Decompositions of the complete graph with an even number of vertices (M.Sc. thesis, McMaster University, Hamilton, 1997).
  • [3] S. El-Zanati and C. Vanden Eynden, Factorizations of $K_{m,n}$ into spanning trees, Graphs Combin. 15 (1999) 287-293, doi: 10.1007/s003730050062.
  • [4] D. Fronček, Cyclic decompositions of complete graphs into spanning trees, Discuss. Math. Graph Theory 24 (2004) 345-353, doi: 10.7151/dmgt.1235.
  • [5] D. Fronček, Bi-cyclic decompositions of complete graphs into spanning trees, Discrete Math. 303 (2007) 1317-1322, doi: 10.1016/j.disc.2003.11.061.
  • [6] D. Fronček, P. Kovár, T. Kovárová and M. Kubesa, Factorizations of complete graphs into caterpillars of diameter 5, submitted for publication.
  • [7] D. Fronček and T. Kovárová, 2n-cyclic labelings of graphs, Ars Combin., accepted.
  • [8] D. Fronček and M. Kubesa, Factorizations of complete graphs into spanning trees, Congr. Numer. 154 (2002) 125-134.
  • [9] J.A. Gallian, A dynamic survey of graph labeling, Electronic Journal of Combinatorics, DS6 (2007).
  • [10] S.W. Golomb, How to number a graph, in: Graph Theory and Computing, ed. R.C. Read (Academic Press, New York, 1972) 23-37.
  • [11] P. Hrnciar and A. Haviar, All trees of diameter five are graceful, Discrete Math. 233 (2001) 133-150, doi: 10.1016/S0012-365X(00)00233-8.
  • [12] M. Kubesa, Factorizations of complete graphs into [n,r,s,2] -caterpillars of diameter 5 with maximum center, AKCE Int. J. Graphs Combin. 1 (2004) 135-147.
  • [13] M. Kubesa, Spanning tree factorizations of complete graphs, J. Combin. Math. Combin. Comput. 52 (2005) 33-49.
  • [14] M. Kubesa, Factorizations of complete graphs into [r,s,2,2] -caterpillars of diameter 5, J. Combin. Math. Combin. Comput. 54 (2005) 187-193.
  • [15] M. Kubesa, Graceful trees and factorizations of complete graphs into non-symmetric isomorphic trees, Util. Math. 68 (2005) 79-86.
  • [16] M. Kubesa, Trees with α-labelings and decompositions of complete graphs into non-symmetric isomorphic spanning trees, Discuss. Math. Graph Theory 25 (2005) 311-324, doi: 10.7151/dmgt.1284.
  • [17] M. Kubesa, Factorizations of complete graphs into [n,r,s,2] -caterpillars of diameter 5 with maximum end, AKCE Int. J. Graphs Combin. 3 (2006) 151-161.
  • [18] G. Ringel, Problem 25, Theory of Graphs and its Applications, Proceedings of the Symposium held in Smolenice in June 1963 (Prague, 1964) 162.
  • [19] G. Ringel, A. Llado and O. Serra, Decomposition of complete bipartite graphs into trees, DMAT Research Report 11 (1996) Univ. Politecnica de Catalunya.
  • [20] A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (Intl. Symp. Rome 1966), Gordon and Breach, Dunod, Paris, 1967, 349-355.
  • [21] S.L. Zhao, All trees of diameter four are graceful, Graph Theory and its Applications: East and West (Jinan, 1986), Ann. New York Acad. Sci., New York 576 (1989) 700-706.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1417
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