IJPAM: Volume 120, No. 3 (2018)

Title

EDGE TRIMAGIC GRACEFUL LABELING OF GRAPHS

Authors

M. Regees$^1$, J.A. Jose Ezhil$^2$, T. Shyla Isac Mary$^3$
$^1$Department of Mathematics
Malankara Catholic College
Mariagiri, Kaliakavilai - 629153, Tamilnadu, INDIA
$^2$Department of Mathematics
Nesamony Memorial Christian College
Marthandam-629165,Tamilnadu, INDIA
$^3$Department of Mathematics
Nesamony Memorial Christian College
Marthandam-629165,Tamilnadu, INDIA

Abstract

A $(p,q)$ graph G is called edge trimagic total if there exists a bijection $f : V(G) \cup E(G) \to \lbrace 1, 2, 3,..., p+q \rbrace$ such that for each edge $xy$ in $E(G)$ the value of $f(x)+f(xy)+f(y)$ = $K_{1}$ or $K_{2}$ or $K_{3}$. $G$ is called edge trimagic graceful if there exists a bijection $f : V(G) \cup E(G) \to \lbrace 1, 2, 3,..., p+q \rbrace$ such that for each edge $xy$ in $E(G)$, $\vert f(x) - f(xy) + f(y) \vert$ = $c_{1}$ or $c_{2}$ or $c_{3}$, where $c_{1}$, $c_{2}$, and $c_{3}$ are constants. In this paper, we introduce edge trimagic graceful labeling of some graphs and proved that the square graph $P_n^2$, $(P_{n};S_{1})$ and the comp $P_{n} \odot K_{1}$ are edge trimagic graceful graphs.

History

Received: October 25, 2017
Revised: January 13, 2018
Published: January 14, 2019

AMS Classification, Key Words

AMS Subject Classification: 05C78
Key Words and Phrases: graph, labeling, magic, trimagic

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Bibliography

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How to Cite?

DOI: 10.12732/ijpam.v120i3.16 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: 3
Pages: 487 - 496


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