IJPAM: Volume 112, No. 5 (2017)

Title

NEIGHBOURLY IRREGULAR $S$-VALUED GRAPHS

Authors

M. Rajkumar$^1$, M. Chandramouleeswaran$^2$
$^{1,2}$Department of Mathematics
Saiva Bhanu Kshtriya College
Aruppukottai, 626101, INDIA

Abstract

Paul Erdős and others studied the notion of locally irregular and highly irregular graphs. Recently, we studied the notion of$S$-valued graphs and regularity on$S$-valued graphs. In this paper, we introduce the notion of irregularity conditions on $S$-valued graphs and we prove some simple but interesting properties.

History

Received: December 110, 2016
Revised: January 22, 2017
Published: March 30, 2017

AMS Classification, Key Words

AMS Subject Classification: 05C07, 05C05, 05C25, 16Y60
Key Words and Phrases: $S$- regular graph, weight $S$- irregular graph, weight $S$- vertex irregular graph , neighbourly weight $S$- irregular graphs

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Bibliography

1
Albertson P(1997), The Irregularity of Graphs, Ars Combinatoria 46 : 219 - 225.

2
Rajkumar.M , jeyalakshmi.S and Chandramouleeswaran.M, Semiring-Valued Graphs, International Journal of Math. Sci. and Engg. Appls. , Vol.9 (III) , 2015,141-152.

3
Jeyalakshmi.S, Rajkumar.M and Chandramouleeswaran.M, Regularity on $S$-Valued Graphs, GJPAM, ISSN 0973-1768, vol (II),No.5 (2015), PP.2971 - 2978.

4
Rajkumar.M and Chandramouleeswaran, Degree Regular $S$-Valued Graphs, MSIRJ,ISSN 2278-8697 , vol(4) , issue 2 (2015), PP. 326-328.

5
Erdős.P and P.J.Kelly, The minimal Regular Graph containing a given Graph, Amer. Math. Monthly 70 (1963) 1074-1075.

6
Y.Alavi,Gary Chatrand, F.R.K.Chung, Paul Erdős,R.L.graham, O.R.Oeller munn, Highly Irregular Graphs, Journal of Graph Theory, Vol 11,no.2 235- 249 (1987)-C. 1987 by John wiley and sons.inc.

How to Cite?

DOI: 10.12732/ijpam.v112i5.3 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: 112
Issue: 5
Pages: 23 - 30


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