i
f
uit
,
1, 1
ti
f
ui
t
20, 1
ti
f
ui
t
,
2,1
i
f
vit
1, 1
ti
f
vi
t
,
20,1
ti
f
vi
t
Then

2
f
v01
ff
vv 2t
 and
122,
ff
ee t02
f
e t1,

Hence f is a mean cordial labeling.
Case (2):
d 31 mon
31nt
Let
i
v1in . Assign labels to the vertices and
(
1
i
u

n
u
) as in case (1). Then assign the label 0
and 1 to the vertices and . Here
n
v
1,22
f
v012
ff
vv t,t and
022,
ff
ee t and

121
f
et
Hence f is a mean cordial labeling.
Case (3):
d 32 mon
32.nt
Let
i (1in Assign labels to the vertices i
u &
v2
) as in case (1). Then assign the label 0,
2 and 0, 1 to the vertices u and respec-
tively. Here
1,
n
u
nn1,
n
vv
02
f
vt2,
and
 
122t1
ff
vv
01
fff
eee221.t
 Hence f is a mean cor-
dial labeling.
Theorem 2.14: PnΘ2K1 is mean cordial.
0
1
1
1
1
1
11
1
0
0
0
0
0
0
0
2
2
2
2
2
2
2
2
0
Figure 2. Mean cordial labeling of S(K1,6).
Copyright © 2012 SciRes. OJDM
R. PONRAJ ET AL.
Copyright © 2012 SciRes. OJDM
148
Let
2, ,, :1
ni
VKuvui n
 and
Proof: Let Pn be the Path 12 Let vi and wi be
the pendant vertices which are adjacent to
.
n
uu u
,1 .
i
uin
2, ,:1
nii
EKuuvuin
 . 2,1
K
and 2,2
K
are mean
cordial by Theorem 2.5 and 2.8 respectively. Assume
. Suppose f is a mean cordial labeling of 2,n
2n
K
.
Clearly either
0fu
or Without loss
generality we can assume so that

fv

0
0.
fu
0.fv
Case (1): n is even.
Define

0, 12
in
fu i
2
1, 12
ni
n
fu i





0 mod 3nCase (1):

0, 12
in
fv i
3.tn
Then 0or
f
ett
Let 1, a contradiction
since the size of 2,n
K
is 6.t

1, 12
in
fw i
od 31 mnCase (2): ce
Let n = 3t + 1. Here again a contradic-
tion.

0
ft,
2
2, 12
ni
n
fv i




 Case (3):
2 mod 3n
0or
f
ett
2,n
Let n = 3t + 2. Here 1, again a con-
tradiction to the size of
K
.
2
2, 12
ni
n
fw i





3. Conclusion
Then and
  
012
fff
vvv
 
01,12.eneen
n

fff
In this paper we introduced the concept of mean cordial
labeling and studied the mean cordial labeling behavior
of few standard graph. The authors are of the opinion that
the study of mean cordial labeling behavior of graph ob-
tained from standard graphs using the graph operation
shall be quite interesting and also will lead to newer re-
sults.
Hence f is a mean cordial labeling.
Case (2): n is odd.
Define

1
0, 12
in
fu i

1
2
1
1, 12
ni
n
fu i





4. Acknowledgements

3
0, 12
in
fvi
 The authors are thankful to the referee for their valuable
comments and suggestions.

3
1, 12
in
fwi

REFERENCES
11
22
0
nn
fv fw

 

 
 
 
[1] J. A. Gallian, “A Dynamic Survey of Graph Labeling,”
Electronic Journal of Combinatorics, Vol. 18, 2011, pp.
1-219.
11
22
1, 2
nn
fv fw

 

 
 
 
[2] I. Cahit, “Cordial Graphs: A Weaker Version of Graceful
and Harmonious Graphs,” Ars Combinatoria, Vol. 23, No.
3, 1987, pp. 201-207.
11
22
1
2, 12
nn
ii
n
fv fwi







[3] M. Sundaram, R. Ponraj and S. Somosundram, “Product
Cordial Labeling of Graph,” Bulletin of Pure and Applied
Sciences, Vol. 23, No. 1, 2004, pp. 155-162.
Then and
  
012
fff
vvv
 
01,12.eneen
n

fff
[4] F. Harary, “Graph Theory,” Addision Wisely, New Delhi,
1969.
Hence f is a mean cordial labeling.
Theorem 2.15: The 2,n
K
is a mean cordial iff 2.n
Proof: