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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 51 | Number 1 | Year 2017 | Article Id. IJMTT-V51P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V51P502

A linear-time Algorithm for Paired Neighbhourhood Set on Circular-Arc Graphs


Saranya C. R., K. S. P. Sowndarya, Y. Lakshmi Naidu
Abstract

The basic difference between a dominating set of a graph and neighbourhood set of a graph is, dominating set covers the vertices of the graph.

Keywords
Algorithm, paired neighbourhood set, circular-arc graph.
References

[1] Min Chih Lin, Jayme L. Szwarcfiter, “Characterizations and recognition of circular arc graphs and subclasses: A survey”, Discrete Mathematics, vol. 309, pp. 5618 – 5635, (2009).
[2] Chig-Chi Lin, Hai-Lun Tu, “A linear-time algorithm for Paired –domination on Circular-arc graphs”, Theoretical Computer Science, vol. 591, pp. 99 – 105, (2015).
[3] T. Haynas, P. Slater, “Paired-domination in graphs”, Networks, vol. 32, pp.199 -206 , (1998).
[4] M.S. Chang, “Efficient algorithms for the domination problems on interval and circular-arc graphs”, SIAM Journal on Computing, vol. 27, pp.1671-1694, (1998).
[5] T.C.E. Cheng, L.Y. Kang, C.T. Ng, “Paired domination on interval and circular-arc graphs”, Discrete Applied Mathematics, vol. 155(16), pp. 2077-2086, (2007).
[6] E. Sampath Kumar, P.S. Neeralagi, “The line neighbhourhood number of a graph”, Indian journal of Pure and Applied Mathematics, vol. 17, pp. 142-149, (1986).
[7] B. Maheshwari, Y. Lakshmi Naidu, L. Nagamuni Reddy, “A. Sudhakaraiah, A Polynomial Time algorithm for finding a minimum Independent neighbhourhood set of an interval graph”, Graph Theory Notes of New York XLVI, pp.9-12, (2004).
[8] Y. Lakshmi Naidu, C.R. Saranya, “Paired Neighbhourhood set on Interval graphs”, International Journal of Pure and Engineering Mathematics, vol. 4, pp. 21-26, (2016).

Citation :

Saranya C. R., K. S. P. Sowndarya, Y. Lakshmi Naidu, "A linear-time Algorithm for Paired Neighbhourhood Set on Circular-Arc Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 51, no. 1, pp. 12-15, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V51P502

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