Homepage for the Graph Labelling Problems and New Results


I have introduced cordial labelling of trees and graphs in 1987 as weakened version of the less tractable graceful, harmonious and magic labellings. This page is the first step to give information on open problems, recent results on cordial and related graph labelling problems e.g., equitable, h-cordial, A-cordial and graceful, harmonious and magic labellings. If you know any paper not in the list or have a labelling problem please inform us for the inclusion here.

We hope that in a near future we will have down-loadable preprint service for the new results. For suggestions and comments write directly to me at

Department of Computer Science & Engineering
European University of Lefke
Guzelyurt , North Cyprus (via Mersin 10, Turkey)

or e-mail: cahit@management.cc.emu.edu.tr
ica@lefke.edu.tr


Problems Section
RP-1-97: Strong graceful labeling of the comet trees , (November 1997).
RP-1-98: Embedding trees gracefully onto the triangular grids, (March 1998)


Papers on Cordial and Equitable Graphs authored by I. Cahit:


  • Cordial graphs: A weaker version of graceful and harmonious graphs, Ars Combinatoria, 23 (1987), 210-207.MR88f:05104, Zbl.Math.616.05056.
  • On cordial and 3-equitable labellings of graphs, Utilitas Math.,37,(1990),189-197. MR 91I:05103, Zbl.Math.714.05053.
  • Status of graceful tree conjecture in 1989, Topics in Combinatorics and Graph Theory (Oberwolfach, 1990), 175-184, Physica, Heidelberg,1990. MR 92a:05113, Zbl.Math.714.05050.
  • Recent results and open problems on cordial graphs, Contemporary Methods in Graph Theory,209-230, Bibliographisches Inst., Mannheim, 1990. MR 92h:05118, Zbl.Math.721.05052.
  • Equitable tree labellings, Ars Combinatoria, 40, 1995, 279-286. MR 96I:05148, Zbl.Math.839.05081.
  • E-Cordial Graphs, (with R. Yilmaz), Ars Combinatoria. , August 1997.
  • E_k Cordial Graphs, (with R. Yilmaz), Ars Combinatoria, 54, (2000), pp. 119-127.
  • Some totally modular cordial graphs, Discussiones Mathematicae Graph Theory, 22, 2002, 247-258.

Papers on Cordial and Equitable Graphs authored by the other researchers (as of January 1997):

  • E. Seah, "On the construction of cordial graphs", Ars. Combin. 31,1991,249-254. MR 92d:05141, Zbl.Math.732.05047.
  • M. Hovey, "A-cordial graphs", Discrete Math., 93, 1991, 183-194.MR 93c:05102, Zbl. Math.753.05059.
  • Y.H. Lee, H.M. Lee, G.J. Chang, "Cordial labelings of graphs", Chinese J. Math., 20, 1992, 3, 263-273. MR 93h:05142, Zbl.Math.760.05076.
  • J. Wojciechowski, Equitable labelings of cycle, J. of Graph Theory, 17, 1993, 4, 531-547. MR 94I:05085, Zbl.Math.781.05046.
  • Z. Szaniszlo, "k-equitable labellings of cycles and some other graphs", Ars Combin., 37, 1994, 49-63. MR 95c:05108, Zbl.Math.805.05073.
  • S-C. Shee, "The cordiality of the path-union of n copies of a graph", Discrete Math., 151, 1996, 1-3, 221-229. MR 97b:05134, Zbl.Math.960.42311.
  • S. M. Lee , A. Liu, "A construction of cordial graphs from smaller cordial graphs", Ars Combin., 32, 1991, 209-214. MR 93e:05087, Zbl.Math.755.05086.
  • Y. S. Ho, S.M. Lee, S.C. Shee, "Cordial labellings of unicyclic graphs and generalized Petersen graphs", Congr. Numer.,68,1989, 109-122. MR 90f:05126, Zbl.Math.672.05078.
  • W. W. Kirchherr, "On the cordiality of some specific graphs", Ars Combin., 31, 1991, 127-138. MR 92c:05133, Zbl. Math.
  • Y. S. Ho, S.M. Lee, S.C. Shee, "Cordial labellings of the Cartesian product and composition of graphs", Ars Combin., 29, 1990, 169-180. MR 91c:05161, Zbl.Math.716.05029.
  • K. Collins, "Most graphs are edge-cordial", Ars Combin., 30, 1990, 289-295. MR 91j:05091, Zbl.Math.734.05072.
  • H. K. Ng andd S.M. Lee, A Conjecture on Edge-Cordial Trees, Abstracts, Amer. Math. Soc., 9, 286-287, 1988.
  • W. W. Kirchherr, "Algebraic approaches to cordial labeling",Graph theory, combinatorics, algorithms and applications, (San Francisco, CA, 1989), 294-299, SIAM Philadelphia, PA,1991. MR 93f:05082, Zbl.Math.751.05076.
  • W. W. Kirchherr, "NEPS operations on cordial graphs", Discrete Math., 115, 1993, 1-3, 201-209. MR 94e:05210, Zbl.Math. 792.05100.
  • E. Seah, "Further results on the neutrality of graphs", Ars Combin., 35, 1993, A, 209-216. MR 94m:05163.
  • S. Kuo, G.J. Chang, Y.H.H. Kwong, "Cordial labeling of mK_n", Discrete Math.,169(1-3),1997, Zbl.Math 970.40495.
  • M Benson and S.M. Lee, "On cordialness of regular windmill graphs", Congr. Numer., 68, 1989, 49-58. Zbl.Math.684.05041.
  • V.N. Bhat-Nayak Equitable Labelings of Graphs : An Update To appear in the Proceedings of the Conference on Graph Theory and its Applications held at School of Mathematics, Anna University, Chennai 600 025, March 14-16, 2001.
  • V.N. Bhat-Nayak Minimal 4-Equitability of $C_{2n} O K_1$ with (Manisha Acharya) accepted for publication in Ars Combinatoria.
  • V.N. Bhat-Nayak Minimal 3-Equitability of $C_{2n} O K_1$ with (Manisha Acharya) to appear in the Proceedings of National Conference on Discrete Mathematics and its Applications held at M.S. University, Thirunelveli, Jan 5-7, 2000.
  • V.N. Bhat-Nayak Minimal $k$-Equitability of $C_{2n} O K_1, k = 2, 2n$ and Associated Graphs with (Manisha Acharya) sent for publication.
  • V.N. Bhat-Nayak Minimal 6-Equitability of $C_{3n} O K_1, n \equiv 0 (mod ~2)$ with (Manisha Acharya) sent for publication.
  • V.N. Bhat-Nayak Minimal 10-Equitability of $C_{5n} O K_1, n \equiv 0 (mod ~2)$ with (Manisha Acharya) sent for publication.
  • V.N. Bhat-Nayak Minimal n-Equitability of $C_{2n} O K_1m, C_{3n} O K_1$ and $C_{5n}O K_1$ with (Manisha Acharya) to appear in the Proceedings of the conference on Graph Theory and its Applications held at School of Mathematics, Anna University, Chennai, 14-16 March, 2001.
  • V.N. Bhat-Nayak Minimal $k$-Equitability of paths $P_{kn+1}$ with (Manisha Acharya) sent for publication.
  • V.N. Bhat-Nayak 3-Equitability of Olive trees (with Shanta Telang) unpublished.
  • V.N.Bhat-Nayak Cahit- $k$ Equitability of $C_n O K_1, k = n$ to $2n-1$ (with Shanta Telang) to be sent for publication.
  • N.B. Limaye (with Mahesh Andar and Somina Boxwala) Cordial Labelings of Some Wheel Related Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing (JCMCC), Vol.41(2002).
  • N.B. Limaye (with Mahesh Andar and Somina Boxwala) A Note on Cordial Labeling of Multiple Shells, Conference proceedings of International Conference on Number Theory and Combinatorics, October 2000.
  • N.B. Limaye (with Mahesh Andar and Somina Boxwala) On Cordiality of The $t$-Uniform Homeomorphs of Graphs - (I), Accepted for publication in ARS Combinatoria.
  • N.B. Limaye (with Mahesh Andar and Somina Boxwala) On Cordiality of The $t$-Uniform Homeomorphs of Graphs - (II) (Complete Graphs), Accepted for publication in ARS Combinatoria.
  • N.B. Limaye (with Mukund Bapat) Some Families of 3 - Equitable Graphs, Accepted for publication in JCMCC.
  • N.B. Limaye (with Mahesh Andar and Somina Boxwala) On the Cordiality of The $t$-ply $P_t(u, v), Sent for publication.
  • N.B. Limaye (with Mahesh Andar and Somina Boxwala) On the Cordiality of Elongated $t$-plys, Sent for publication.
  • G. Chartrand, S-Min Lee and P. Zhang, Randomly Cordial Graphs, to appear.
  • M. Andar, S. Boxwala and N. Limaye, Cordial labelings of some wheel related graphs, preprint.
  • M. Andar, S. Boxwala and N. Limaye, A note on cordial labelings of multiple shells, preprint.
  • C. Barrientos, New families of equitable graphs, preprint.
  • C. Barrientos, Equitable labelings of corona graphs, preprint.
  • C. Barrientos, I. Dejter and H. Hevia, Equitable labelings of forests, Combin. and Graph Theory, 1 (1995) 1-26.
  • C. Barrientos and H. Hevia, On $2$-equitable labelings of graphs, Notas de la Sociedad de Matemetica de Chile, XV (1996) 97-110.
  • M. Benson and S.M. Lee, On cordialness of regular windmill graphs, Congress. Numer., 68 (1989) 45-58.
  • N. Cairnie and K. Edwards, The computational complexity of cordial and equitable labelling, Discrete Math., 216 (2000) 29-34.
  • J. W. Krussel, Equitable labelling of complete bipartite graphs, Ars Combin., to appear.
  • H. Y. Lee, H. M. Lee and G. J. Chang, Cordial labelings of graphs, Chinese J. Math., 20 (1992) 263-273.
  • M. Seoud and A.E. I. Abdel Maqsoud, On 3-equitable and magic labelings, preprint.
  • M. Seoud and A.E. I. Abdel Maqsoud, On cordial and balanced labelings of graphs, J. Egyptian Math. Soc.,7 (1999) 127135.
  • D. Speyer and Z. Szaniszlo, Every tree is $3$-equitable, Discrete Math.,220, (2000) 283-289.
  • R. Tao, On $k$-cordiality of cycles, crowns and wheels, Systems Sci. Math. Sci., 11 (1998) 227--229.
  • D. Vickrey, $k$-equitable labelings of complete bipartite and multipartite graphs, Ars Combin., 54 (2000) 65-85.
  • J. Wojciechowski, Equitable labelings of cycles, J. Graph Theory, 17 (1993) 531-547.
  • A. Godbole, C. Miller and D. Ramas, Almost all random graphs are cordial, Horizons in Combinatorics, 16th Sharks Lecture Series, Vanderbilt Univ., TN, USA, May 21-24 2001.