Hiindex LOGO

Research Article

Energy of Certain Planar Graphs


Author(s): M.Chris Monica , S.Santhakumar
Affiliation: Department of Mathematics,Loyola college,Chennai
Year of Publication: 2014
Source: International Journal of Computing Algorithm
     
×

Scholarly Article Identity Link


HTML:


File:


Citation: M.Chris Monica, S.Santhakumar. "Energy of Certain Planar Graphs." International Journal of Computing Algorithm 3.1 (2014): 65-67.

Abstract:
The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G of its adjacency matrix. The Laplacian energy LE(G) of a graph G is the sum of absolute values of its Laplacian eigenvalues. In this paper, we provide a MATLAB program,to calculate the energy and Laplacian energy of certain planar graphs namely n-regular caterpillar and Necklace.


Keywords Energy, Laplacian energy,n-regular caterpillar, Necklace.


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

@article{Ene1458866, author = {M.Chris Monica,S.Santhakumar}, title = {Energy of Certain Planar Graphs}, journal={International Journal of Computing Algorithm}, volume={3}, issue={1}, issn = {2278-2397}, year = {2014}, publisher = {Scholarly Citation Index Analytics-SCIA}

  • [1] Andries E. Brouwer, Willem H. Haemers., Spectra of Graphs, Springer, 2011.
  • [2] Balakrishnan. R, The Energy of a Graph, Linear Algebra Appl., Vol.387, pp. 287-295,2004
  • [3] Bharati Rajan, Sudeep Stephen, Cyriac Grigorious., On Laplacian Energy of certain Mesh DerivedNetworks, International Journal of Computer Appl (0975-8887), 2012.
  • [4] Bondy. J. A, Murty.U. S. R., Graph Theory with Applications, Elsevier SciencePublishing Co., Inc, 1974.
  • [5] Clemens Heuberger, Stephan G. Wagner., Chemical Trees Minimizing Energy andHosoya Index, Algorithmen and Mathematische Modellierung, 2008.
  • [6] Chris Godsil, Gordon Royle, Algebraic Graph Theory, Springer-Verlag, 2001.
  • [7] Curtis C. W, I. Reiner, Representation Theory of Finite Groups and Associative Algebras, Wiley Interscience, 1962.
  • [8] Cvetkovic. D, Doop. M, Gutman. I, A. Torgaser., Resent results in the theory of GraphSpectra, Annals of Discrete Mathematics, 1988.
  • [9] Cvetkovic. D, Gutman. I., Croat. Chem.Acta 49, Vol. 105, 1977.
  • [10] Cvetkovic. D, Doop M, Sachs. H., Spectra of Graphs - Theory and Applications, Academic Press, 1980.
  • [11] Cvetkovic. D, Gutman I., Selected Topics on Applications of Graph Spectra, Vol.519.17, No. 082, 2011.
  • [12] Gutman. I, The Energy of a Graph, Ber, Math, Statist.Sekt. Forshungszentrum graz, Vol. 103, 1978.
  • [13] Gutman.I, The Energyof a Graph: Old and New Results, Algebraic Combinatorics and Applications, Springer, Berlin, pp. 196 – 211, 2001.
  • [14] Gutman. I, Hou. Y, Walikar. H. B, Ramane. H. S, HampiholiP. R., No H ̈ckal graph ishyperenergetic, J. Serb. Chem. Soc.,Vol. 65, No. 11,pp. 799-801, 2000.
  • [15] Gutman. I, Zhou. B., Laplacian energy of a graph, Lin. Algebra Appl., Vol.414,pp. 29–37, 2006.
  • [16] Gholam Hossein Fath-Tabar and Ali Reza Ashrafi, Some remarks on Laplacian Eigenvaluesand Laplacian Energy of a Graph, Mathematical Communications, Vol.15, pp. 443-451,2010.
  • [17] Igor Shparlinski, On the Energy of some Circulant Graphs, Linear Algebra Appl., Vol. 414, pp. 378 – 382, 2006.
  • [18] Indulal. G., A Note on Energy of some Graphs, Math communication in mathematical and in Computer chemistry, Vol.59, pp. 269-274, 2008.
  • [19] Michael WilliamNewman, The Laplacian Spectrum of Graphs, 2000.
  • [20] Rao Li., Some Lower Bounds for Laplacian Energy of Graphs, International Journal of Contemporary Mathematical Sciences,Vol.4, pp. 219-223, 2009.
  • [21] Saraswathi Vishveshwara, Brinda K. V. Kannan N., Protein Structure: Insights From Graph Theory, Journal of Theoretical and Computational Chemistry, Vol. 1, No. 1, pp. 187-211, 2002.
  • [22] Yuanping Zhang, Xiaogang Liu, Xuerong Yong, Which wheel graphs are determined by theirLaplacian spectra ?,Computers and Mathematics with Appl., Vol 58, pp 1887 – 1890, 2009.
  • <?xml version='1.0' encoding='UTF-8'?> <record> <language>eng</language> <journalTitle>International Journal of Computing Algorithm</journalTitle> <eissn>2278-2397 </eissn> <publicationDate>2014</publicationDate> <volume>3</volume> <issue>1</issue> <startPage>65</startPage> <endPage>67</endPage> <documentType>article</documentType> <title language='eng'>Energy of Certain Planar Graphs</title> <authors> <author> <name>M.Chris Monica</name> </author> </authors> <abstract language='eng'>The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G of its adjacency matrix. The Laplacian energy LE(G) of a graph G is the sum of absolute values of its Laplacian eigenvalues. In this paper, we provide a MATLAB program,to calculate the energy and Laplacian energy of certain planar graphs namely n-regular caterpillar and Necklace.</abstract> <fullTextUrl format='pdf'>http://www.hindex.org/2014/p588.pdf</fullTextUrl> <keywords language='eng'> <keyword>Energy, Laplacian energy,n-regular caterpillar, Necklace.</keyword> </keywords> </record>

    { "@context":"http://schema.org", "@type":"publication-article","identifier":"http://www.hindex.org/2014/article.php?page=588", "name":"Energy of Certain Planar Graphs", "author":[{"name":"M.Chris Monica "}], "datePublished":"2014", "description":"The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G of its adjacency matrix. The Laplacian energy LE(G) of a graph G is the sum of absolute values of its Laplacian eigenvalues. In this paper, we provide a MATLAB program,to calculate the energy and Laplacian energy of certain planar graphs namely n-regular caterpillar and Necklace.", "keywords":["Energy, Laplacian energy,n-regular caterpillar, Necklace."], "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>S.Santhakumar</dc:contributor> <dc:contributor></dc:contributor> <dc:contributor></dc:contributor> <dc:creator>M.Chris Monica</dc:creator> <dc:date>2014</dc:date> <dc:description>The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G of its adjacency matrix. The Laplacian energy LE(G) of a graph G is the sum of absolute values of its Laplacian eigenvalues. In this paper, we provide a MATLAB program,to calculate the energy and Laplacian energy of certain planar graphs namely n-regular caterpillar and Necklace.</dc:description> <dc:identifier>2014SCIA316F0588</dc:identifier> <dc:language>eng</dc:language> <dc:title>Energy of Certain Planar Graphs</dc:title> <dc:type>publication-article</dc:type> </oai_dc:dc>

    { "identifier": "2014SCIA316F0588", "abstract": "The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G of its adjacency matrix. The Laplacian energy LE(G) of a graph G is the sum of absolute values of its Laplacian eigenvalues. In this paper, we provide a MATLAB program,to calculate the energy and Laplacian energy of certain planar graphs namely n-regular caterpillar and Necklace.", "author": [ { "family": "M.Chris Monica,S.Santhakumar" } ], "id": "588", "issued": { "date-parts": [ [ 2014 ] ] }, "language": "eng", "publisher": "Scholarly Citation Index Analytics-SCIA", "title": " Energy of Certain Planar Graphs", "type": "publication-article", "version": "3" }