IJPAM: Volume 118, No. 4 (2018)

Title

A NOTE ON TOTAL NEIGHBORHOOD PRIME LABELING

Authors

Rajesh Kumar T.J.$^1$, Mathew Varkey T.K.$^2$
$^{1,2}$Department of Mathematics
T.K.M College of Engineering
Kollam, Kerala, INDIA

Abstract

A graph G with vertex set V(G) is said to have a prime labeling if its vertices can be labeled with distinct integers 1,2,3,...,$\vert V\vert$ such that for each $xy\epsilon E(G)$ the labels assigned to x and y are relatively prime.A graph that admits a prime labeling is called a prime graph.In this paper,we introduce a new type of labeling called total neighborhood prime labeling. A graph which admits total neighbourhood prime labeling is called total neighbourhood prime graph.We studied the total neighbourhood prime labeling of paths and cycles.We proved that every path $P_n$ and every cycle $C_n$ if n is even and $n \ncong 2 mod(4)$ are total neighbourhood prime graphs. We also prove that the comb graph is total neighbourhood prime graph.

History

Received: May 24, 2017
Revised: January 12, 2018
Published: May 23, 2018

AMS Classification, Key Words

AMS Subject Classification: 05C78
Key Words and Phrases: total neighborhood prime labeling, paths, cycles, comb graph

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How to Cite?

DOI: 10.12732/ijpam.v118i4.14 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: 118
Issue: 4
Pages: 1007 - 1013


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