IJPAM: Volume 116, No. 3 (2017)

Title

ZUMKELLER CORDIAL LABELING
OF CYCLE RELATED GRAPHS

Authors

B.J. Murali$^1$, K. Thirusangu$^2$, B.J. Balamurugan$^3$
$^1$Research and Development Centre
Bharathiar University
Coimbatore, 641 046, Tamil Nadu, INDIA
$^2$Department of Mathematics
SIVET College
Gowrivakkam, Chennai, 600 073, Tamil Nadu, INDIA
$^3$School of Advanced Sciences
VIT University
Chennai Campus
Vandalur-Kelambakkam Road, Chennai, 600 127, Tamil Nadu, INDIA

Abstract

Let $G = (V, E)$ be a graph with vertex set $V$ and edge set $E$. A Zumkeller cordial labeling of the graph $G$ can be defined as an injective function $f : V \to N$ such that the induced function $f^* :
E \to \{0, 1\}$ defined by $f^*(xy) = f(x) f(y)$ is 1 if $f(x) f(y)$ is a Zumkeller number and 0 otherwise with the condition $\vert e_{f^*}(0)
- e_{f^*}(1)\vert \leq 1$ where $e_{f^*}(0)$ and $e_{f^*}(1)$ denote respectively the number of edges of $G$ with label 0 and the number of edges of $G$ with label 1 under $f^*$. We make use of a technique of generating Zumkeller numbers and the concept of cordiality in the labeling of graphs. In this paper we show the existence of Zumkeller cordial labeling of cycle related graphs.

History

Received: 2017-04-24
Revised: 2017-07-12
Published: October 25, 2017

AMS Classification, Key Words

AMS Subject Classification: 05C78
Key Words and Phrases: graphs, Zumkeller numbers, Zumkeller labeling, Zumkeller cordial labeling

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How to Cite?

DOI: 10.12732/ijpam.v116i3.7 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: 2017
Volume: 116
Issue: 3
Pages: 617 - 627


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