HUB-INTEGRITY OF SPLITTING GRAPH AND DUPLICATION OF GRAPH ELEMENTS

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.

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  • 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.