Product rosy labeling of graphs

Dalibor Fronček

Discussiones Mathematicae Graph Theory (2008)

  • Volume: 28, Issue: 3, page 431-439
  • ISSN: 2083-5892

Abstract

top
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.

How to cite

top

Dalibor Fronček. "Product rosy labeling of graphs." Discussiones Mathematicae Graph Theory 28.3 (2008): 431-439. <http://eudml.org/doc/270192>.

@article{DaliborFronček2008,
abstract = {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.},
author = {Dalibor Fronček},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {graph decomposition; graph labeling},
language = {eng},
number = {3},
pages = {431-439},
title = {Product rosy labeling of graphs},
url = {http://eudml.org/doc/270192},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Dalibor Fronček
TI - Product rosy labeling of graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2008
VL - 28
IS - 3
SP - 431
EP - 439
AB - 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.
LA - eng
KW - graph decomposition; graph labeling
UR - http://eudml.org/doc/270192
ER -

References

top
  1. [1] R.E.L. Aldred and B.D. McKay, Graceful and harmonious labellings of trees, Bull. Inst. Combin. Appl. 23 (1998) 69-72. Zbl0909.05040
  2. [2] P. Eldergill, Decompositions of the complete graph with an even number of vertices (M.Sc. thesis, McMaster University, Hamilton, 1997). 
  3. [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. Zbl0935.05075
  4. [4] D. Fronček, Cyclic decompositions of complete graphs into spanning trees, Discuss. Math. Graph Theory 24 (2004) 345-353, doi: 10.7151/dmgt.1235. Zbl1060.05080
  5. [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. Zbl1118.05079
  6. [6] D. Fronček, P. Kovár, T. Kovárová and M. Kubesa, Factorizations of complete graphs into caterpillars of diameter 5, submitted for publication. Zbl1220.05098
  7. [7] D. Fronček and T. Kovárová, 2n-cyclic labelings of graphs, Ars Combin., accepted. 
  8. [8] D. Fronček and M. Kubesa, Factorizations of complete graphs into spanning trees, Congr. Numer. 154 (2002) 125-134. Zbl1021.05083
  9. [9] J.A. Gallian, A dynamic survey of graph labeling, Electronic Journal of Combinatorics, DS6 (2007). Zbl0953.05067
  10. [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. [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. Zbl0986.05088
  12. [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. Zbl1062.05121
  13. [13] M. Kubesa, Spanning tree factorizations of complete graphs, J. Combin. Math. Combin. Comput. 52 (2005) 33-49. Zbl1067.05059
  14. [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. Zbl1080.05075
  15. [15] M. Kubesa, Graceful trees and factorizations of complete graphs into non-symmetric isomorphic trees, Util. Math. 68 (2005) 79-86. Zbl1106.05076
  16. [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. Zbl1105.05056
  17. [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. Zbl1120.05070
  18. [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. [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. [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. [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. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.