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Characterization of Circular-Arc Overlap Graphs with Domination Number Two

by A. Sudhakaraiah, V. Raghava Lakshmi
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 41 - Number 3
Year of Publication: 2012
Authors: A. Sudhakaraiah, V. Raghava Lakshmi
10.5120/5519-7539

A. Sudhakaraiah, V. Raghava Lakshmi . Characterization of Circular-Arc Overlap Graphs with Domination Number Two. International Journal of Computer Applications. 41, 3 ( March 2012), 6-9. DOI=10.5120/5519-7539

@article{ 10.5120/5519-7539,
author = { A. Sudhakaraiah, V. Raghava Lakshmi },
title = { Characterization of Circular-Arc Overlap Graphs with Domination Number Two },
journal = { International Journal of Computer Applications },
issue_date = { March 2012 },
volume = { 41 },
number = { 3 },
month = { March },
year = { 2012 },
issn = { 0975-8887 },
pages = { 6-9 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume41/number3/5519-7539/ },
doi = { 10.5120/5519-7539 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:28:38.473224+05:30
%A A. Sudhakaraiah
%A V. Raghava Lakshmi
%T Characterization of Circular-Arc Overlap Graphs with Domination Number Two
%J International Journal of Computer Applications
%@ 0975-8887
%V 41
%N 3
%P 6-9
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

A graph is a circular arc graph if it is the intersection graph of a finite set of arcs on a circle. A circular-arc overlap graph is a special case of circular arc graph; it is an overlap graph defined for a set of arcs on a circle. That is, there is one arc for each vertex of G and two vertices in G are adjacent in G if and only if the corresponding arcs intersect and one is not contained in the other. In this paper, we emphasize on characterizing circular-arc overlap graphs (CAOG) as partite graphs k2,2, k3,3, kn,n and k2,2,2. . ,2. Furthermore, we do characterize circular-arc overlap graphs having any pair of vertices of the graph as a minimal dominating set in terms of the neighborhood of the arcs of the graph. Apart from that, we present an algorithm to check whether the given CAOG has every pair of vertices as minimal dominating set or not.

References
  1. O. Ore. Theory of Graphs, Ann. Math. Soc. Colloq. Publ. 38. Providence, 1962
  2. C. Berge. Graphs and Hypergraphs, North-Holland, Amsterdam 1973.
  3. E. J. Cockayne and S. T. Hedetniemi. Networks 7(1977), 247-261.
  4. H. B. Walikar, B. D. Acharya and E. Sampathkumar. Recent Developments in the theory oh Dominatio in Graphs, In: MRI Lecture Notes No. 1. Allahabad 1979.
  5. S. R. Jayaram. Indian J. purepl. Math. , 28(1) : 43-46, January 1997.
Index Terms

Computer Science
Information Sciences

Keywords

Circular-arc Overlap Graphs Partite Graphs Dominating Set Minimal Dominating Set Domination Number

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