IJPAM: Volume 120, No. 4 (2018)

Title

EDGE TRIMAGIC TOTAL LABELING OF
CYCLE RELATED GRAPHS

Authors

C. Jayasekaran$^1$, S. Robinson Chellathurai$^2$, J. Little Flower$^3$
$^1$Department of Mathematics
Pioneer Kumaraswamy College
Nagercoil - 629003, TamilNadu, INDIA
$^2$Department of Mathematics
Scott Christian College
Nagercoil – 629 003, Tamilnadu, INDIA
$^3$Department of Mathematics
Arignar Anna College
Aralvaimozhi - 629 301, TamilNadu, INDIA

Abstract

An edge trimagic total labeling of a graph $G = (V, E)$ with $p$ vertices and $q$ edges is a bijection $f: V(G)\cup E(G)\rightarrow \{1, 2, \ldots, p+q\}$ if for each edge $uv\in E(G)$, the value of $f(u)+f(uv)+f(v)$ is either $k_1$ or $k_2$ or $k_3$. In this paper, we prove that the Closed helm $CH_n$, Antiprism $A_n$ and Square graph of $C_n$ are edge trimagic total and super edge trimagic total labeling.

History

Received: September 3, 2017
Revised: January 22, 2019
Published: January 27, 2019

AMS Classification, Key Words

AMS Subject Classification: 05C78
Key Words and Phrases: edge trimagic total labeling, bijection, closed helm, antiprism, square graph

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1
A. Ahmad, On Vertex Irregular Total Labeling of Convex Polytope Graphs, Util. Math., 89 (2012) 69-78.

2
J.B. Babujee, On Edge Bimagic Labeling, Journal of Combinatorics Information & System Sciences, 1-4 (2004) 239-244 .

3
Frank Harary, Graph theory, Narosa Publishing House, New Delhi 2001.

4
G.V. Ghodasara and S.M Vaghasiya, Product Cordial Labeling of Graphs Related to Helm, Closed Helm and Gear Graphs, Intern. Journal of Pure and Applied Mathematics, 91(4) (2014) 495-504.

5
C. Jayasekaran, M. Regees and C. Davidraj, Edge trimagic labeling of some graphs, Intern. J. Combinatorial Graph Theory and Applications 6(2) (2013) 175-186.

6
6. C. Jayasekaran and J. Little Flower, On Edge Trimagic Labeling of Umbrella, Dumb bell and Circular Ladder Graphs, Annals of Pure and Applied Mathematics, 13(1) (2017) 73-87.

7
C. Jayasekaran and J. Little Flower, Edge Trimagic Total Labeling of Mobius Ladder, Book and Dragon Graphs, Annals of Pure and Applied Mathematics, 13(2) (2017) 151-163.

8
Joseph A. Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics, 16 (2013)#DS6.

9
A.Kotzing and A. Rosa, Magic valuations of finite graphs, Canad. Math. Bull., 13 (1970) 451-461.

10
M. Regees and C. Jayasekaran, More Results On Edge Trimagic Labeling of Graphs, International Journal of Mathematical Archive, 4(11) (2013), 247-255.

11
M. Regees and C. Jayasekaran, Super Edge Trimagic Total Labeling of Generalized Prism and Web Graphs, Journal of Discrete Math. Sci. & Cryptography, 19 (2016) no.1, 81-92.

12
M. Regees and C. Jayasekaran, Super Edge Trimagic Total Labeling of Square of a cycle and Gear Graphs, Mathematical Sciences International Research Journal, 2 (2015) 113-115.

13
J. Sedlacek, Problem 27: in Theory of Graphs and its Applications, Proc. Symposium Smolenice, June (1963) 163-167.

How to Cite?

DOI: 10.12732/ijpam.v120i4.1 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 120
Issue: 4
Pages: 511 - 519


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).