A Note on McPherson Number of Graphs

Authors

  • C. Susanth Department of Mathematics, Research & Development Centre, Bharathiar University, Coimbatore 641046, Tamilnadu
  • Sunny Joseph Kalayathankal Department of Mathematics, Kuriakose Elias College, Mannanam, Kottayam 686561, Kerala
  • N. K. Sudev Department of Mathematics, Vidya Academy of Science and Technology, Thrissur 680501, Kerala

DOI:

https://doi.org/10.26713/jims.v8i2.409

Keywords:

Vertex explosion, McPherson number, McPherson recursion

Abstract

By the explosion of a vertex \(v\) in a graph \(G\), we mean drawing edges from \(v\) to all other vertices in \(G\) that are not already adjacent to it. The recursive concept of vertex explosions is called the McPherson recursion. The McPherson number of a graph is the minimum number of vertex explosions required in \(G\) so that the resultant graph becomes a complete graph. In this paper, we determine the McPherson number of a given graph.

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References

J.A. Bondy and U.S.R. Murty, Graph Theory, Springer, New York (2008).

J. Clark and D.A. Holton, A First Look at Graph Theory, Allied Pub., New Delhi (1991).

N. Deo, Graph Theory with Applications to Engineering and Computer Science, PHI Learning, Delhi (1974).

F. Harary, Graph Theory, Addison Wesley Pub., Reading, Massachusetts (1969).

J. Kok, C. Susanth and S.J. Kalayathankal, A study on linear Jaco graphs, Journal of Informatics and Mathematical Sciences 7 (2) (2015), 69–80.

J. Kok and C. Susanth, Introduction to the McPherson number (Upsilon(G)) of a simple connected graph, Pioneer J. Math. Math. Sci. 13 (2) (2014), 91–102.

D.B. West, Introduction to Graph Theory, Pearson Education Asia, New Delhi (2002).

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Published

2016-05-24
CITATION

How to Cite

Susanth, C., Kalayathankal, S. J., & Sudev, N. K. (2016). A Note on McPherson Number of Graphs. Journal of Informatics and Mathematical Sciences, 8(2), 123–127. https://doi.org/10.26713/jims.v8i2.409

Issue

Vol. 8 No. 2 (2016)

Section

Research Articles

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