On Twin Edge Colorings of Graphs

Eric Andrews; Laars Helenius; Daniel Johnston; Jonathon VerWys; Ping Zhang

Discussiones Mathematicae Graph Theory (2014)

  • Volume: 34, Issue: 3, page 613-627
  • ISSN: 2083-5892

Abstract

top
A twin edge k-coloring of a graph G is a proper edge coloring of G with the elements of Zk so that the induced vertex coloring in which the color of a vertex v in G is the sum (in Zk) of the colors of the edges incident with v is a proper vertex coloring. The minimum k for which G has a twin edge k-coloring is called the twin chromatic index of G. Among the results presented are formulas for the twin chromatic index of each complete graph and each complete bipartite graph

How to cite

top

Eric Andrews, et al. "On Twin Edge Colorings of Graphs." Discussiones Mathematicae Graph Theory 34.3 (2014): 613-627. <http://eudml.org/doc/268302>.

@article{EricAndrews2014,
abstract = {A twin edge k-coloring of a graph G is a proper edge coloring of G with the elements of Zk so that the induced vertex coloring in which the color of a vertex v in G is the sum (in Zk) of the colors of the edges incident with v is a proper vertex coloring. The minimum k for which G has a twin edge k-coloring is called the twin chromatic index of G. Among the results presented are formulas for the twin chromatic index of each complete graph and each complete bipartite graph},
author = {Eric Andrews, Laars Helenius, Daniel Johnston, Jonathon VerWys, Ping Zhang},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {edge coloring; vertex coloring; factorization},
language = {eng},
number = {3},
pages = {613-627},
title = {On Twin Edge Colorings of Graphs},
url = {http://eudml.org/doc/268302},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Eric Andrews
AU - Laars Helenius
AU - Daniel Johnston
AU - Jonathon VerWys
AU - Ping Zhang
TI - On Twin Edge Colorings of Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2014
VL - 34
IS - 3
SP - 613
EP - 627
AB - A twin edge k-coloring of a graph G is a proper edge coloring of G with the elements of Zk so that the induced vertex coloring in which the color of a vertex v in G is the sum (in Zk) of the colors of the edges incident with v is a proper vertex coloring. The minimum k for which G has a twin edge k-coloring is called the twin chromatic index of G. Among the results presented are formulas for the twin chromatic index of each complete graph and each complete bipartite graph
LA - eng
KW - edge coloring; vertex coloring; factorization
UR - http://eudml.org/doc/268302
ER -

References

top
  1. [1] L. Addario-Berry, R.E.L. Aldred, K. Dalal and B.A. Reed, Vertex colouring edge partitions, J. Combin. Theory (B) 94 (2005) 237-244. doi:10.1016/j.jctb.2005.01.001[Crossref] Zbl1074.05031
  2. [2] M. Anholcer, S. Cichacz and M. Milaniˇc, Group irregularity strength of connected graphs, J. Comb. Optim., to appear. doi:10.1007/s10878-013-9628-6[Crossref] Zbl1316.05078
  3. [3] G. Chartrand, M.S. Jacobson, J. Lehel, O.R. Oellermann, S. Ruiz and F. Saba, Irregular networks, Congr. Numer. 64 (1988) 187-192. 
  4. [4] G. Chartrand, L. Lesniak and P. Zhang, Graphs & Digraphs: 5th Edition (Chapman & Hall/CRC, Boca Raton, FL, 2010). 
  5. [5] G. Chartrand and P. Zhang, Chromatic Graph Theory (Chapman & Hall/CRC, Boca Raton, FL, 2008). doi:10.1201/9781584888017[Crossref] Zbl1169.05001
  6. [6] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 16 (2013) #DS6. Zbl0953.05067
  7. [7] R.B. Gnana Jothi, Topics in Graph Theory, Ph.D. Thesis, Madurai Kamaraj University (1991). 
  8. [8] S.W. Golomb, How to number a graph, in: Graph Theory and Computing R.C. Read (Ed.), (Academic Press, New York, 1972) 23-37. Zbl0293.05150
  9. [9] R. Jones, Modular and Graceful Edge Colorings of Graphs, Ph.D. Thesis, Western Michigan University (2011). 
  10. [10] R. Jones, K. Kolasinski, F. Fujie-Okamoto and P. Zhang, On modular edge-graceful graphs, Graphs Combin. 29 (2013) 901-912. doi:10.1007/s00373-012-1147-1[Crossref] Zbl1268.05174
  11. [11] R. Jones, K. Kolasinski and P. Zhang, A proof of the modular edge-graceful trees conjecture, J. Combin. Math. Combin. Comput. 80 (2012) 445-455. Zbl1247.05207
  12. [12] M. Karoński, T. Luczak and A. Thomason, Edge weights and vertex colours, J. Combin. Theory (B) 91 (2004) 151-157. doi:10.1016/j.jctb.2003.12.001[Crossref] Zbl1042.05045
  13. [13] A. Rosa, On certain valuations of the vertices of a graph, in: Theory of Graphs, Proc. Internat. Symposium Rome 1966 (Gordon and Breach, New York 1967) 349-355. 
  14. [14] V.G. Vizing, On an estimate of the chromatic class of a p-graph, Diskret. Analiz. 3 (1964) 25-30 (in Russian). 

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.