Let G(V, E) be a graph with order p and size q. The graph G is called as an even-odd harmonious graph if there exists an 1-1 map f:V → {1, 3, 5, …, 2p − 1} and a bijective map f:E → {0, 2, …, 2(q − 1)} such that f(e = uv) = (f(u) + f(v))(mod 2q). This computation of assigning the numbers to the vertices and edges of G is called an even-odd harmonious labeling of G. This article shows the existence of this labeling to certain family of graphs obtained through graph operations viz., i) Union of graphs ii) Superimposing and iii) Corona.

1.
B.D.
Acharya
,
S.M.
Hegde
,
Arithmetic Graphs. J. Graph Theory
, Vol.
14
, No.
3
,
275
299
, (
1990
).
2.
N. Adalin
Beatress
,
P.B.
Sarasija
,
Even–odd harmonious graphs
,
International Journal of Mathematics and Soft Computing
, Vol.
5
, No.
1
,
23
29
, (
2015
).
3.
A. Amara
Jothi
,
N.G.
David
and
J. Baskar
Babujee
,
E-super vertex bimagic graph labeling
,
International Journal of Pure and Applied Mathematics
, Vol.
109
, No.
9
,
19
27
,(
2016
).
4.
R.
Frucht
,
F.
harary
,
On the corona of two graphs
,
Aequationes mathematicae
, Vol.
4
,
322
325
, (
1970
).
5.
R.L.
Graham
,
N.J.A.
Sloane
,
On additive bases and harmonious graphs
,
SIAM Journal on Algebraic and Discrete Methods
, Vol.
1
, No.
4
,
382
404
, (
1980
).
6.
F.
Harary
,
Graph Theory
,
Addison-Wesley
,
Reading Mass
, (
1972
).
7.
Joseph A.
Gallian
,
A Dynamic Survey of Graph Labeling
,
The Electronic Journal of Combinatorics
,
17
,
DS6
, (
2016
).
8.
N. Lakshmi
Prasana
,
K.
Saravanthi
,
Nagalla
Sudhakar
,
Applications of Graph Labeling in Major Areas of computing science
.
International Journal of Research in Computer and Communication Technology
, Vol.
3
, No.
8
, (
2014
).
9.
Z.
Liang
,
Z.
Bai
Z.
On The Odd Harmonious Graphs With Applications
,
J. Appl. Math. Comput.
,
29
,
105
116
, (
2009
).
10.
A.
Rosa
, On Certin Valuations of the vertices of a Graph, In Theory of Graphs (
Internat. Sympos. Rome
.
1966
),
Gordan and Breach
,
Newyork, Dunod, Paris
,
349
359
, (
1967
).
11.
J.
Renuka
,
P.
Balaganesan
,
P.
Selvaraju
, and
V.
Balaji
,
On harmonious labeling
,
American Journal of Mathematical Science and Applications
Vol.
1
, No.
1
,
55
60
, (
2013
).
12.
P. B.
Sarasija
,
R.
Binthiya
,
Even harmonious graphs with applications
,
International Journal of Computer Science and Information Security
, Vol.
9
, No.
7
,
161
163
, (
2011
).
This content is only available via PDF.
You do not currently have access to this content.