The open hub number of a graph

Downloads

DOI:

https://doi.org/10.26637/MJM0804/0006

Abstract

Let \(G=(V, E)\) be a connected graph. A subset \(H\) of \(V\) is called a hub set of \(G\) if for any two distinct vertices \(u, v \in V-H\), there exists a \(u-v\) path \(P\) in \(G\) such that all the internal vertices of \(P\) are in \(\mathrm{H}\). A hub set \(H\) of \(V\) is called an open hub set if the induced sub graph \(\langle H\rangle\) has no isolated vertices. The minimum cardinality of an open hub set of \(G\) is called the open hub number of \(G\) and is denoted by \(h_O(G)\). In this paper, we present several basic results on the open hub number.

Keywords:

Open hub set, Open hub number

Mathematics Subject Classification:

Matheatics
  • Pages: 1375-1377
  • Date Published: 01-10-2020
  • Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)

F. Harary, Graph Theory, Addison-Wesley Pub House, 1963.

C. Gary and Z. Ping, Introduction to Graph Theory, Tata McGraw-Hill, 2006.

W. Matthew, The hub number graphs, International Journal of Mathematics and Computer Science, 1(2006), $117-$ 124.

W.H. Teresa, T.H. Stephan and J.S. Peter, Fundamentals of Domination in Graphs, Marcel Dekker, Inc, 2008.

G. Tracy, A.H. Stephan and J. Adam, The hub number of a graph, Information Processing Letters, 108(2008), 226-228.

  • NA

Similar Articles

1 2 3 4 5 > >> 

You may also start an advanced similarity search for this article.

Metrics

Metrics Loading ...

Published

01-10-2020

How to Cite

Ragi Puthan Veettil, and T.V. Ramakrishnan. “The Open Hub Number of a Graph”. Malaya Journal of Matematik, vol. 8, no. 04, Oct. 2020, pp. 1375-7, doi:10.26637/MJM0804/0006.