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,
hcordial, Acordial 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 downloadable 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
email: cahit@management.cc.emu.edu.tr
ica@lefke.edu.tr
Problems Section
RP197: Strong graceful
labeling of the comet trees , (November 1997).
RP198:
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),
210207.MR88f:05104, Zbl.Math.616.05056.
 On
cordial and 3equitable labellings of graphs,
Utilitas Math.,37,(1990),189197. MR 91I:05103,
Zbl.Math.714.05053.
 Status
of graceful tree conjecture in 1989, Topics in
Combinatorics and Graph Theory (Oberwolfach,
1990), 175184, Physica, Heidelberg,1990. MR
92a:05113, Zbl.Math.714.05050.
 Recent
results and open problems on cordial graphs,
Contemporary Methods in Graph Theory,209230,
Bibliographisches Inst., Mannheim, 1990. MR
92h:05118, Zbl.Math.721.05052.
 Equitable
tree labellings, Ars Combinatoria, 40, 1995,
279286. MR 96I:05148, Zbl.Math.839.05081.
 ECordial
Graphs, (with R. Yilmaz), Ars Combinatoria. ,
August 1997.
 E_k
Cordial Graphs, (with R. Yilmaz), Ars
Combinatoria, 54, (2000), pp. 119127.
 Some
totally modular cordial graphs, Discussiones
Mathematicae Graph Theory, 22, 2002, 247258.
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. 31,1991,249254. MR
92d:05141, Zbl.Math.732.05047.
 M.
Hovey, "Acordial graphs", Discrete
Math., 93, 1991, 183194.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, 263273. MR 93h:05142,
Zbl.Math.760.05076.
 J.
Wojciechowski, Equitable labelings of cycle, J.
of Graph Theory, 17, 1993, 4, 531547. MR
94I:05085, Zbl.Math.781.05046.
 Z.
Szaniszlo, "kequitable labellings of cycles
and some other graphs", Ars Combin., 37,
1994, 4963. MR 95c:05108, Zbl.Math.805.05073.
 SC.
Shee, "The cordiality of the pathunion of n
copies of a graph", Discrete Math., 151,
1996, 13, 221229. 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, 209214. 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,
109122. MR 90f:05126, Zbl.Math.672.05078.
 W.
W. Kirchherr, "On the cordiality of some
specific graphs", Ars Combin., 31, 1991,
127138. 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, 169180. MR 91c:05161, Zbl.Math.716.05029.
 K.
Collins, "Most graphs are
edgecordial", Ars Combin., 30, 1990,
289295. MR 91j:05091, Zbl.Math.734.05072.
 H.
K. Ng andd S.M. Lee, A Conjecture on EdgeCordial
Trees, Abstracts, Amer. Math. Soc., 9, 286287,
1988.
 W.
W. Kirchherr, "Algebraic approaches to
cordial labeling",Graph theory,
combinatorics, algorithms and applications, (San
Francisco, CA, 1989), 294299, SIAM Philadelphia,
PA,1991. MR 93f:05082, Zbl.Math.751.05076.
 W.
W. Kirchherr, "NEPS operations on cordial
graphs", Discrete Math., 115, 1993, 13,
201209. MR 94e:05210, Zbl.Math. 792.05100.
 E.
Seah, "Further results on the neutrality of
graphs", Ars Combin., 35, 1993, A, 209216.
MR 94m:05163.
 S.
Kuo, G.J. Chang, Y.H.H. Kwong, "Cordial
labeling of mK_n", Discrete
Math.,169(13),1997, Zbl.Math 970.40495.
 M
Benson and S.M. Lee, "On cordialness of
regular windmill graphs", Congr. Numer., 68,
1989, 4958. Zbl.Math.684.05041.
 V.N.
BhatNayak 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 1416, 2001.
 V.N.
BhatNayak Minimal 4Equitability of $C_{2n} O
K_1$ with (Manisha Acharya) accepted for
publication in Ars Combinatoria.
 V.N.
BhatNayak Minimal 3Equitability 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 57, 2000.
 V.N.
BhatNayak Minimal $k$Equitability of $C_{2n} O
K_1, k = 2, 2n$ and Associated Graphs with
(Manisha Acharya) sent for publication.
 V.N.
BhatNayak Minimal 6Equitability of $C_{3n} O
K_1, n \equiv 0 (mod ~2)$ with (Manisha Acharya)
sent for publication.
 V.N.
BhatNayak Minimal 10Equitability of $C_{5n} O
K_1, n \equiv 0 (mod ~2)$ with (Manisha Acharya)
sent for publication.
 V.N.
BhatNayak Minimal nEquitability 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, 1416 March, 2001.
 V.N.
BhatNayak Minimal $k$Equitability of paths
$P_{kn+1}$ with (Manisha Acharya) sent for
publication.
 V.N.
BhatNayak 3Equitability of Olive trees (with
Shanta Telang) unpublished.
 V.N.BhatNayak
Cahit $k$ Equitability of $C_n O K_1, k = n$ to
$2n1$ (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, SMin 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) 126.
 C.
Barrientos and H. Hevia, On $2$equitable
labelings of graphs, Notas de la Sociedad de
Matemetica de Chile, XV (1996) 97110.
 M. Benson
and S.M. Lee, On cordialness of regular windmill
graphs, Congress. Numer., 68 (1989) 4558.
 N. Cairnie
and K. Edwards, The computational complexity of
cordial and equitable labelling, Discrete Math.,
216 (2000) 2934.
 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) 263273.
 M. Seoud
and A.E. I. Abdel Maqsoud, On 3equitable 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) 127—135.
 D. Speyer
and Z. Szaniszlo, Every tree is $3$equitable,
Discrete Math.,220, (2000) 283289.
 R. Tao, On
$k$cordiality of cycles, crowns and wheels,
Systems Sci. Math. Sci., 11 (1998) 227229.
 D.
Vickrey, $k$equitable labelings of complete
bipartite and multipartite graphs, Ars Combin.,
54 (2000) 6585.
 J.
Wojciechowski, Equitable labelings of cycles, J.
Graph Theory, 17 (1993) 531547.
 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 2124 2001.
