Graph labeling is a way of assigning integers to vertices or edges of a graph that satisfy certain conditions. One of graph labeling is odd harmonious labeling. Let G = G(p, q) be a graph that have p vertices and q edges. An odd harmonious labeling of G is an injective function f from the set of vertices of G to the set { 0, 1, 2, …, 2q - 1} such that the induced function f*, where f*: E(G) → {1, 3, 5, … , 2q - 1}, and f* (uv) = f(u) + f(v) for every edge uv ∈ E(G), is bijective. A snake graph k(G) is a graph obtained from a path on k edges by replacing each edge by a graph isomorphic to G. If such labeling exists, then G is said to be odd harmonious. In this paper we show that snake graph k(G) is odd harmonious for some graph G.
REFERENCES
1.
R.
Diestel
, Graph Theory
(Electronic Edition), Third, (Spinger-Verlag Heidelberg
, New York
, 2005
).2.
J. A.
Gallian
, “A dynamic survey of graph labeling
,” in Electron Journal of Combinatorics
1(Dynamic Surveys)
, (2020
).3.
Z. H.
Liang
and Z. L.
Bai
, “On the odd harmonious graphs with applications
,” in Journal of Applied Mathematics and Computing
29
(1
), 105
–116
(2009
).4.
M. E.
Abdel-Aal
, “Odd Harmonious Labeling of Cyclic Snakes
,” in International journal on applications of graph theory in wireless ad hoc networks and sensor networks (GRAPH-HOC)
5
(3
), 1
–11
(2013
).5.
M. E.
Abdel-Aal
, “New Families of Odd Harmonious Graphs
,” in International Journal of Soft Computing Mathematics and Control
3
(1
), 1
–13
(2014
).6.
F.
Firmansah
, Pelabelan harmonis ganjil pada gabungan graf ular dan graf ular berlipat
, March (2016
).7.
F.
Firmansah
F, “The Odd Harmonious Labeling on Variation of the Double Quadrilateral Windmill Graphs
,” in Jurnal ILMU DASAR
18
(2
), 109
–118
(2017
).8.
F.
Firmansah
, “Pelabelan Harmonis Ganjil pada Graf Ular Jaring Berlipat
,” in Sainmatika: Jurnal Ilmu Matematika dan Ilmu Pengetahuan Alam
17
(1
), 1
–8
(2020
).9.
P.
Jeyanthi
and S.
Philo
, “Odd harmonious labeling of plus graphs
,” in Bulletin of the International Mathematics virtual Institute
7
(3
), 515
–526
(2017
).10.
P.
Jeyanthi
and S.
Philo
, “Odd Harmonious Labeling of Some New Graphs
,” in Southeast Asian Bulletin of Mathematics
, 509
–523
(2019
).11.
P.
Jeyanthi
and S.
Philo
, “Odd harmonious labeling of some cycle related graphs
,” in Proyecciones
35
, 85
–89
(2016
).12.
P.
Jeyanthi
and S.
Philo
, “Odd Harmonious Labeling Of Certain Graphs
,” in JASC: Journal of Applied Science and Computations VI(IV)
, 1224
–1232
(2019
).13.
P.
Jeyanthi
and S.
Philo
, “Some Results on Odd Harmonious Labeling of Graphs
,” in Journals / Bull.
9
, 567
–576
(2019
).14.
P.
Jeyanthi
and S.
Philo
, “Odd Harmonious Labeling of Subdivided Shell Graphs
,” in Int. J. Comput. Sci. Eng.
7
(2019
), 5
p. 76
–80
.15.
P.
Jeyanthi
and S.
Philo
, “Odd harmonious labeling of some classes of graphs
,” in Cubo
22
(2020
), 3 p. 299
–314
.16.
P.
Jeyanthi
, S.
Philo
and K. A.
Sugeng
, “Odd harmonious labeling of some new families of graphs
,” in SUT J. Math.
(2015
) 51
p. 181
–193
.17.
P.
Jeyanthi
, S.
Philo
and M.
Youssef
, “Odd harmonious labeling of grid graph
,” in Proyecciones
38
(3
), 411
–428
(2019
).18.
Saputri G A
Sugeng
K A and Froncek
D
, The Odd Harmonious Labeling of Dumbbell and Generalized Prism Graphs
, AKCE Int. J. Graphs Comb.
, 10
, No. 2
(2013
), 2 p. 221
–228
.
This content is only available via PDF.
© 2022 Author(s).
2022
Author(s)
You do not currently have access to this content.