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Inverse Line Domination Number of Jump Graph

N. Pratap Babu Rao. Published in Applied Mathematics.

Communications on Applied Electronics
Year of Publication: 2017
Publisher: Foundation of Computer Science (FCS), NY, USA
Authors: N. Pratap Babu Rao
10.5120/cae2017652728

Pratap Babu N Rao. Inverse Line Domination Number of Jump Graph. Communications on Applied Electronics 7(11):9-10, December 2017. BibTeX

@article{10.5120/cae2017652728,
	author = {N. Pratap Babu Rao},
	title = {Inverse Line Domination Number of Jump Graph},
	journal = {Communications on Applied Electronics},
	issue_date = {December 2017},
	volume = {7},
	number = {11},
	month = {Dec},
	year = {2017},
	issn = {2394-4714},
	pages = {9-10},
	numpages = {2},
	url = {http://www.caeaccess.org/archives/volume7/number11/788-2017652728},
	doi = {10.5120/cae2017652728},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}
}

Abstract

Let J(G) =(V,E) be a jump graph. Let D is minimum line dominating set in a jump graph E(J(G)). If E-D contains a line dominating set D’ of E(J(G)) then D’ is called an inverse dominating set with respect to D. The cardinality of an inverse line dominating set of a jump graph J(G) is called inverse line dominating set of E(JG)).

In this paper we study theoretic properties of inverse line domination of jump graph and its exact value for some standard graphs. The relation between inverse line domination of jump graph with other parameters is also investigated.

References

  1. O. Ore Theory of Graphs. Amer. Math. Soci . Collq public 38 providence (1962)
  2. F. Harary Graph theory Adition-wesley Reading mass (1969)
  3. V.R. Kulli and S.C. Sigarkanti Inverse domination in Graph Nat. Acad Sci Lett 14 (1991) 473-475.
  4. G. Chatrand, H. Hevia, E.B Jarett, M. Schultz Subgraph distance in graph defined by edges transfers Discrete Math., 170 (1997) 63-79
  5. T. H Haynes, S.T. Hedetinemi and P. J. Slater Fundamentals of Domination in graphs Marcel Dekker Inc, New York (1998)
  6. G.S. Domke, J.E Dumbar and L.R Markus The inverse domination number of a graph Ars. Combin 72 (2004) 149-160.
  7. G. Chatrand and L. Lesniak, Graphs and Digraphs CRC (2004)
  8. P .D. Johnson , D.R. Pries and M.Walsh, On problem of Domke Haynes, Hedetinemi and markus Concerning the inverse domination number AKCEJ Graph Combin.72(2010) 217-222.
  9. A.Frendrup, M.A. Henning, b.Randerath and P. D. vestergoard On conjecture about inverse dominations in Graph Ars combinotorics 95A(2010) 103-111
  10. M. Karthikeyan, A Elumai Edge domination number of jump graphs. Int.. joumal of scientific& Engineering Research, vol6 issue3 (2015).pure and applied maths vol103 No.3 (2015) 477-483
  11. Y. B. Maralabhavi et.al., Domination number of jump graph Intn.Mathematical Forum vol8 (2013) 753-758
  12. S.R. Jayaram Line domination in graph Graphs and combinotorics vol3 (1987) 357-363.
  13. M. Karthikeyan, A. Elumalai Inverse domination number of jump graph. Int. joum.pure and applied maths vol103 No.3 (2015) 477-483 100-102.

Keywords

Graph circumference, diameter, domination, inverse line domination number, jump graph.