IJPAM: Volume 117, No. 3 (2017)

Title

RELATION BETWEEN MCPHERSON NUMBER
AND BLOTTING NUMBER OF GRAPHS

Authors

Johan Kok
Centre for Studies in Discrete Mathematics
Vidya Academy of Science and Technology
Thrissur, Kerala, INDIA

Abstract

The concept of the McPherson number denoted by $\Upsilon(G)$, of a simple, undirected, finite, connected graph $G$ on $n$ vertices was introduced in 2015. The initial notion resulted in a grah $G$ which recursively evolved into a mixed complete graph. Hence, a graph having both edges and arcs resulted. Recently the notion of the blotting number denoted, $\mathfrak{b}(G)$ of a graph $G$ was introduced. This prompted the thinking that the McPherson recursion could rather result in edges instead of arcs, and it was found that $\mathfrak{b}(G)= \Upsilon(\overline{G})$.

History

Received: 2017-05-06
Revised: 2017-11-18
Published: January 15, 2018

AMS Classification, Key Words

AMS Subject Classification: 05C07, 05C20, 05C40, 05C75
Key Words and Phrases: McPherson number, McPherson recursion, blotting number

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Bibliography

1
J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, Macmillan Press, London, 1976.

2
F. Harary, Graph Theory, Addison-Wesley, Reading MA, 1969.

3
J. Kok and C. Susanth, Introduction to the McPherson number, $\Upsilon(G)$ of a simple connected graph, Pioneer Journal of Mathematics and Mathematical Sciences, 13, No. 2 (2015), 91-102.

4
C. Susanth, S.J. Kalayathankal, and N.K. Sudev, A note on McPherson number of graphs, Journal of Informatics and Mathematical Sciences, 8, No. 2 (2016), 123-127.

5
C. Susanth, S.J. Kalayathankal, and N.K. Sudev, A study on blotting number of graphs, Journal of Informatics and Mathematical Sciences, To Appear.

How to Cite?

DOI: 10.12732/ijpam.v117i3.8 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: 117
Issue: 3
Pages: 431 - 435


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