Article Sidebar

Submitted
July 16, 2013
Accepted
May 22, 2014
Published
May 23, 2014
Download
PDF
Statistic
Read Counter : 851 Download : 355

Downloads

Download data is not yet available.

Main Article Content

Abstract

Recently we introduced the concept of minimum dominating energy[21]. Motivatedby this paper,we introduced the concept of minimum dominating distance energyEDd(G) of a graph G and computed minimum dominating distance energies of a Stargraph,Complete graph,Crown graph and Cocktail graphs. Upper and lower boundsfor EDd(G) are also established.

DOI : http://dx.doi.org/10.22342/jims.20.1.133.19-29

Keywords

Minimum dominating set Minimum dominating distance matrix Minimum dominating distance eigenvalues Minimum dominating distance energy of a graph. 1 I

Article Details

Author Biographies

rajesh kanna, Post Graduate Department of Mathematics, Maharanis Science College for Women, Mysore 570005, Karnataka, India./

Asst.Professor,

Post Graduate Department of Mathematics,

DHARMENDRA B N, Post Graduate Department of Mathematics, Maharanis Science College for Women, Mysore 570005, Karnataka, India.

Asst.Professor,

Post Graduate Department of Mathematics,

SRIDHARA G, Post Graduate Department of Mathematics, Maharanis Science College for Women, Mysore 570005, Karnataka, India.

Asst.Professor,

Post Graduate Department of Mathematics,

How to Cite
kanna, rajesh, B N, D., & G, S. (2014). MINIMUM DOMINATING DISTANCE ENERGY OF A GRAPH. Journal of the Indonesian Mathematical Society, 20(1), 19–29. https://doi.org/10.22342/jims.20.1.133.19-29
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. R.B.Bapat, page No.32,Graphs and Matrices,Hindustan Book Agency,(2011).
  2. R.B.Bapat, S.Pati, Energy of a graph is never an odd integer.Bull. Kerala Math.
  3. Assoc. 1, 129 - 132 (2011)
  4. S. B. Bozkurt, A. D. Gungor, B. Zhou, Note on the distance energy of graphs,
  5. MATCH Commun. Math. Comput. Chem. 64 (2010) 129134.
  6. G. Caporossi, E. Chasset, B. Furtula, Some conjectures and properties on distance
  7. energy, Les Cahiers du GERAD G-2009-64 (2009) V+17.
  8. D.Cvetkovic, I.Gutman (eds.),Applications of Graph Spectra (Mathematical Institution,
  9. Belgrade,2009)
  10. D. Cvetkovic, I.Gutman (eds.) Selected Topics on Applications of Graph Spectra,
  11. (Mathematical Institute Belgrade,2011)
  12. A.Graovac, I.Gutman, N.Trinajstic,Topological Approach to the Chemistry of
  13. Conjugated Molecules (Springer, Berlin,1977)
  14. A. D. Gungor, S. B. Bozkurt, On the distance spectral radius and distance energy
  15. of graphs, Lin. Multilin. Algebra 59 (2011) 365370.
  16. I.Gutman,The energy of a graph.Ber. Math-Statist. Sekt. Forschungsz.Graz 103,
  17. -22 (1978)
  18. I.Gutman, X. Li, J.Zhang,in Graph Energy,ed. by M.Dehmer, F.Emmert - Streib.
  19. Analysis of Complex Networks. From Biology to Linguistics (Wiley - VCH, Weinheim,
  20. ,pp. 145 174.
  21. I.Gutman, in The energy of a graph: Old and New Results,ed.by A. Betten,
  22. A. Kohnert, R. Laue, A. Wassermann. Algebraic Combinatorics and Applications
  23. (Springer, Berlin,2001),pp. 196 - 211.
  24. I.Gutman, O.E. Polansky,Mathematical Concepts in Organic Chemistry
  25. (Springer, Berlin,1986)
  26. Huiqing Liu,Mei Lu and Feng Tian,Some upper bounds for the energy of graphs
  27. Journal of Mathematical Chemistry, Vol. 41, No.1, (2007).
  28. A. Ilic, Distance spectra and distance energy of integral circulant graphs, Lin.
  29. Algebra Appl. 433 (2010) 10051014.
  30. G. Indulal, Sharp bounds on the distance spectral radius and the distance energy
  31. of graphs, Lin. Algebra Appl. 430 (2009) 106113.
  32. G. Indulal, I. Gutman, A. Vijayakumar, On distance energy of graphs,MATCH
  33. Commun. Math. Comput. Chem. 60 (2008) 461472.
  34. G. Indulal, I. Gutman, D-Equienergetic self-complementary graphs, Kragujevac
  35. J. Math. 32 (2009) 123131.
  36. J.H. Koolen, V. Moulton, Maximal energy graphs. Adv.Appl. Math. 26,47 - 52
  37. (2001)
  38. M. Liu, A note on D-equienergetic graphs, MATCH Commun. Math. Comput.
  39. Chem. 64 (2010) 125140.
  40. B.J.McClelland, Properties of the latent roots of a matrix: The estimation of
  41. -electron energies.J. Chem. Phys.54, 640 - 643 (1971)
  42. M.R.Rajesh Kanna, B. N. Dharmendra, and G. Sridhara, Minimum Dominating
  43. Energy of a Graph. International Journal of Pure and Applied Mathematics, 85,
  44. No. 4 (2013) 707-718.
  45. H. S. Ramane, I. Gutman, D. S. Revankar, Distance equienergetic
  46. graphs,MATCH Commun. Math. Comput. Chem. 60 (2008) 473484.
  47. H. S. Ramane, D. S. Revankar, I. Gutman, S. B. Rao, B. D. Acharya, H. B.
  48. Walikar, Bounds for the distance energy of a graph, Kragujevac J. Math. 31 (2008)
  50. H. S. Ramane, D. S. Revankar, I. Gutman, H. B. Walikar, Distance spectra
  51. and distance energies of iterated line graphs of regular graphs, Publ. Inst. Math.
  52. (Beograd) 85 (2009) 3946.
  53. D. Stevanovic, G. Indulal, The distance spectrum and energy of the composition
  54. of regular graphs, Appl. Math. Lett. 22 (2009) 11361140.
  55. B. Zhou, A. Ilic, On distance spectral radius and distance energy of
  56. graphs,MATCH Commun. Math. Comput. Chem. 64 (2010) 261280.