On the Monophonic Number of Line Graph

J. Arockia Aruldoss; S. Ganesamurthy

doi:https://doi.org/10.14445/22315373/IJMTT-V23P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 23 | Number 1 | Year 2015 | Article Id. IJMTT-V23P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V23P506

On the Monophonic Number of Line Graph

J. Arockia Aruldoss, S. Ganesamurthy

Abstract

For a connected graph G = (V, E) of order at least 2, a subset S of V is said to be a monophonic set of G if each vertex V of G lies on an x-y monophonic path for some elements x and y in S. The minimum cardinality of a monophonic set of G is the monophonic number of G. In this paper, we obtain the monophonic number of line graph.

Keywords

Monophonic set, monophonic number, monophonic distance, line graph.

References

1. F. Buckley and F. Harary, Distance in Graphs, Addison- Wesley, Redwood City, CA, (1990).
2. A. P. Santhakumaran, P. Titus and K. Ganesamoorthy, On The Monophonic Number of a Graph, J. Appl. Math. & Informatics Vol. 32(2014), No. 1-2, pp. 255 – 266 http://dx.doi.org/10.14317/jami.2014.255
3. A.P. Santhakumaran & S.V. Ullas Chandran, The Monophonic Number of Cartesian Product Graphs, Indiana University Mathematics Journal c, Vol. 61, No. 2 (2012).
4. Douglas B. West, Introduction to Graph theory Second edition, Pearson Education (singapore) Pte. Ltd, Indian Branch.

Citation :

J. Arockia Aruldoss, S. Ganesamurthy, "On the Monophonic Number of Line Graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 23, no. 1, pp. 40-41, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V23P506