Hiindex LOGO

Research Article

Cyclic Resolving Number Of Grid And Augmented Grid Graphs


Author(s): M.Chris Monica , D.Little Femilin Jana
Affiliation: Department of Mathematics,Loyola college,Chennai
Year of Publication: 2013
Source: International Journal of Computing Algorithm
     
×

Scholarly Article Identity Link


HTML:

<a href="http://www.hindex.org/2013/article.php?page=985"><img src="http://www.hindex.org/sai.php/2013SCIA316F0985" alt="SAI"></a>


File:

http://www.hindex.org/2013/p985.pdf


Citation: M.Chris Monica, D.Little Femilin Jana. "Cyclic Resolving Number Of Grid And Augmented Grid Graphs." International Journal of Computing Algorithm 2.2 (2013): 112-114.

Abstract:
For an ordered set W = {w1, w2 … wk}  V G of vertices, we refer to the ordered k-tuple rv  W = dv, w1, dv, w2 … dv, wk as the metric representation of v with respect to W. A set W of a connected graph G is called a resolving set of G if distinct vertices of G have distinct representations with respect to W. A resolving set with minimum cardinality is called a minimum resolving set or a basis. The dimension, dimG, is the number of vertices in a basis for G. By imposing additional constraints on the resolving set, many resolving parameters are formed. In this paper, we introduce cyclic resolving set and find the cyclic resolving number for a grid graph and augmented grid graph.


Keywords Resolving set, Cyclic resolving number, Grid graph, distance


  • BibTex
  • Reference
  • XML
  • JSON
  • Dublin Core
  • CSL

@article{Cyc1398511, author = {M.Chris Monica,D.Little Femilin Jana}, title = {Cyclic Resolving Number Of Grid And Augmented Grid Graphs}, journal={International Journal of Computing Algorithm}, volume={2}, issue={2}, issn = {2278-2397}, year = {2013}, publisher = {Scholarly Citation Index Analytics-SCIA}

  • [1] BharatiRajan, Sonia K.T., Chris Monica M., Conditional Resolvability of Honeycomb and Hexagonal Networks, Mathematics in Computer Science, Vol. 5, pp. 89-99, 2011.
  • [2] BharatiRajan, Albert William, IndraRajasingh, Prabhu S., On Certain Connected Resolving Parameters of Hypercube Networks, Applied Mathematics, Vol. 3, pp. 473-477, 2012.
  • [3] Beerliova Z., Eberhard F., Erlebach T., Hall A., Hoffman M., Mihalák M., Network Discovery and Verification, IEEE, J. Sel. Areas Commun., Vol. 24, No. 12, pp. 2168–2181, 2006.
  • [4] Chartrand G., Eroh L., Johnson M., Oellermann O., Resolvability in Graphs and the Metric Dimension of a graph, Discrete Appl. Math., Vol. 105, pp. 99–113, 2000.
  • [5] Garey M. R., Johnson D. S., Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, NewYork, 1979.
  • [6] Goddard W, Statistic Mastermind Revisited, J. Combin. Math.Combin.Comput., Vol. 51, pp. 215–220, 2004.
  • [7] Harary F., Melter R.A., On the Metric Dimension of a Graph, ArsCombin.,Vol. 2, pp. 191–195, 1976.
  • [8] Johnson M.A., Structure Activity Maps for Visualizing the Graph Variables Arising in Drug Design, J. Biopharm.Stat., Vol. 3, pp. 203–236, 1993.
  • [9] Khuller S., Ragavachari B., Rosenfield A., Landmarks in Graphs, Discret. Appl. Math., Vol. 70, No. 3, pp. 217–229, 1996.
  • [10] Marie Claude Heydemann, Bertrand Ducourthial, Cayley Graphs and Interconnection Networks, Graph Symmetry, NATO ASI Series, Vol. 497, pp. 167-224, 1997.
  • [11] Melter, R.A., Tomcscu I., Metric Bases in Digital Geometry, Comput. Vis. Graph. Image Process., Vol. 25, pp. 113–121, 1984.
  • [12] Mordecai J. Golin,Yiu-Cho Leung,Yajun Wang,Xuerong Yong, Counting Structures in Grid Graphs, Cylinders and Tori Using Transfer Matrices: Survey and New Results, ALENEX / ANALCO, pp. 250-258, 2005.

  • <?xml version='1.0' encoding='UTF-8'?> <record> <language>eng</language> <journalTitle>International Journal of Computing Algorithm</journalTitle> <eissn>2278-2397 </eissn> <publicationDate>2013</publicationDate> <volume>2</volume> <issue>2</issue> <startPage>112</startPage> <endPage>114</endPage> <documentType>article</documentType> <title language='eng'>Cyclic Resolving Number Of Grid And Augmented Grid Graphs</title> <authors> <author> <name>M.Chris Monica</name> </author> </authors> <abstract language='eng'>For an ordered set W = {w1, w2 … wk}  V G of vertices, we refer to the ordered k-tuple rv  W = dv, w1, dv, w2 … dv, wk as the metric representation of v with respect to W. A set W of a connected graph G is called a resolving set of G if distinct vertices of G have distinct representations with respect to W. A resolving set with minimum cardinality is called a minimum resolving set or a basis. The dimension, dimG, is the number of vertices in a basis for G. By imposing additional constraints on the resolving set, many resolving parameters are formed. In this paper, we introduce cyclic resolving set and find the cyclic resolving number for a grid graph and augmented grid graph.</abstract> <fullTextUrl format='pdf'>http://www.hindex.org/2013/p985.pdf</fullTextUrl> <keywords language='eng'> <keyword>Resolving set, Cyclic resolving number, Grid graph, distance</keyword> </keywords> </record>

    { "@context":"http://schema.org", "@type":"publication-article","identifier":"http://www.hindex.org/2013/article.php?page=985", "name":"Cyclic Resolving Number Of Grid And Augmented Grid Graphs", "author":[{"name":"M.Chris Monica "}], "datePublished":"2013", "description":"For an ordered set W = {w1, w2 … wk}  V G of vertices, we refer to the ordered k-tuple rv  W = dv, w1, dv, w2 … dv, wk as the metric representation of v with respect to W. A set W of a connected graph G is called a resolving set of G if distinct vertices of G have distinct representations with respect to W. A resolving set with minimum cardinality is called a minimum resolving set or a basis. The dimension, dimG, is the number of vertices in a basis for G. By imposing additional constraints on the resolving set, many resolving parameters are formed. In this paper, we introduce cyclic resolving set and find the cyclic resolving number for a grid graph and augmented grid graph.", "keywords":["Resolving set, Cyclic resolving number, Grid graph, distance"], "schemaVersion":"https://schema.org/version/3.3", "includedInDataCatalog":{ "@type":"DataCatalog", "name":"Scholarly Citation Index Analytics-SCIA", "url":"http://hindex.org"}, "publisher":{"@type":"Organization", "name":"Scientific Communications Research Academy" } }

    <?xml version='1.0' encoding='utf-8'?> <oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd"> <dc:contributor>D.Little Femilin Jana</dc:contributor> <dc:contributor></dc:contributor> <dc:contributor></dc:contributor> <dc:creator>M.Chris Monica</dc:creator> <dc:date>2013</dc:date> <dc:description>For an ordered set W = {w1, w2 … wk}  V G of vertices, we refer to the ordered k-tuple rv  W = dv, w1, dv, w2 … dv, wk as the metric representation of v with respect to W. A set W of a connected graph G is called a resolving set of G if distinct vertices of G have distinct representations with respect to W. A resolving set with minimum cardinality is called a minimum resolving set or a basis. The dimension, dimG, is the number of vertices in a basis for G. By imposing additional constraints on the resolving set, many resolving parameters are formed. In this paper, we introduce cyclic resolving set and find the cyclic resolving number for a grid graph and augmented grid graph.</dc:description> <dc:identifier>2013SCIA316F0985</dc:identifier> <dc:language>eng</dc:language> <dc:title>Cyclic Resolving Number Of Grid And Augmented Grid Graphs</dc:title> <dc:type>publication-article</dc:type> </oai_dc:dc>

    { "identifier": "2013SCIA316F0985", "abstract": "For an ordered set W = {w1, w2 … wk}  V G of vertices, we refer to the ordered k-tuple rv  W = dv, w1, dv, w2 … dv, wk as the metric representation of v with respect to W. A set W of a connected graph G is called a resolving set of G if distinct vertices of G have distinct representations with respect to W. A resolving set with minimum cardinality is called a minimum resolving set or a basis. The dimension, dimG, is the number of vertices in a basis for G. By imposing additional constraints on the resolving set, many resolving parameters are formed. In this paper, we introduce cyclic resolving set and find the cyclic resolving number for a grid graph and augmented grid graph.", "author": [ { "family": "M.Chris Monica,D.Little Femilin Jana" } ], "id": "985", "issued": { "date-parts": [ [ 2013 ] ] }, "language": "eng", "publisher": "Scholarly Citation Index Analytics-SCIA", "title": " Cyclic Resolving Number Of Grid And Augmented Grid Graphs", "type": "publication-article", "version": "3" }