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HUB-INTEGRITY OF SPLITTING GRAPH AND DUPLICATION OF GRAPH ELEMENTS

Year 2016, Volume: 6 Issue: 2, 289 - 297, 01.12.2016

Abstract

The hub-integrity of a graph G = V G ;E G is denoted as HI G and dened by HI G = minfjSj + m G S ; S is a hub set of Gg, where m G S is the order of a maximum component of G S. In this paper, we discuss hub-integrity of splitting graph and duplication of an edge by vertex and duplication of vertex by an edge of some graphs.

References

  • Barefoot,C.A., Entringer,R. and Swart,H., (1987), Vulnerability in Graphs-A Comparative Survey, J. Combin. Math. Combin. Comput., 1, pp. 13-22.
  • Dundar,P. and Aytac,A., (2004), Integrity of Total Graphs via Certain Parameters, Mathematical Notes, 76(5), pp. 665-672.
  • Grossman,J.W., Harary,F. and Klawe,M., (1979), Generalized ramsey theorem for graphs, X: Double stars, Discrete Mathematics, 28, pp. 247-254.
  • Harary,F., (1969), Graph Theory, Addison Wesley, Reading Mass.
  • Mahde,S.S., Mathad,V. and Sahal,A.M., (2015), Hub-integrity of graphs, Bulletin of International Mathematical Virtual Institute, 5 , pp. 57-64.
  • Sampathkumar,E. and Walikar,H.B., (1980-81), On splitting graph of a graph, J. Karnatak University Science, 25 and 26(combined), pp. 13-16.
  • Vaidya,S.K. and Bijukumar,L., (2010), Some New Families of Mean Graphs, Journal of Mathematics Research, 2(3), pp. 169-176.
  • Vaidya,S.K. and Kothari,N.J., (2012), Some New Results on Domination Integrity of Graphs, Open Journal of Discrete Mathematics, 2(3), pp. 96-98.
  • Vaidya,S.K. and Kothari,N., (2013), Domination integrity of splitting graph of path and cycle, Hindawi Publishing Corporation, ISRN Combinatorics, Article ID 795427, pp. 7.
  • Walsh,M., (2006), The hub number of graphs, International Journal of Mathematics and Computer Science, 1 , pp. 117-124.
Year 2016, Volume: 6 Issue: 2, 289 - 297, 01.12.2016

Abstract

References

  • Barefoot,C.A., Entringer,R. and Swart,H., (1987), Vulnerability in Graphs-A Comparative Survey, J. Combin. Math. Combin. Comput., 1, pp. 13-22.
  • Dundar,P. and Aytac,A., (2004), Integrity of Total Graphs via Certain Parameters, Mathematical Notes, 76(5), pp. 665-672.
  • Grossman,J.W., Harary,F. and Klawe,M., (1979), Generalized ramsey theorem for graphs, X: Double stars, Discrete Mathematics, 28, pp. 247-254.
  • Harary,F., (1969), Graph Theory, Addison Wesley, Reading Mass.
  • Mahde,S.S., Mathad,V. and Sahal,A.M., (2015), Hub-integrity of graphs, Bulletin of International Mathematical Virtual Institute, 5 , pp. 57-64.
  • Sampathkumar,E. and Walikar,H.B., (1980-81), On splitting graph of a graph, J. Karnatak University Science, 25 and 26(combined), pp. 13-16.
  • Vaidya,S.K. and Bijukumar,L., (2010), Some New Families of Mean Graphs, Journal of Mathematics Research, 2(3), pp. 169-176.
  • Vaidya,S.K. and Kothari,N.J., (2012), Some New Results on Domination Integrity of Graphs, Open Journal of Discrete Mathematics, 2(3), pp. 96-98.
  • Vaidya,S.K. and Kothari,N., (2013), Domination integrity of splitting graph of path and cycle, Hindawi Publishing Corporation, ISRN Combinatorics, Article ID 795427, pp. 7.
  • Walsh,M., (2006), The hub number of graphs, International Journal of Mathematics and Computer Science, 1 , pp. 117-124.
There are 10 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Sultan Senan Mahde This is me

Veena Mathad This is me

Publication Date December 1, 2016
Published in Issue Year 2016 Volume: 6 Issue: 2

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