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Distance majorization integrity of graphs

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The concept of distance majorization integrity is introduced as a new measure of the stability of a graph G and it is de ned as DMI(G) = min{|S| + m(G - S)}, where S is a distance majorization set and m(G - S) is the order of a maximum component of G - S. The distance majorization integrity of some graphs is obtained. The relations between distance majorization integrity and other parameters are determined. Also a distance majorization integrity of corona of some graphs are computed

Abstract

The concept of distance majorization integrity is introduced as a new measure of the stability of a graph G and it is de ned as DMI(G) = min{|S| + m(G - S)}, where S is a distance majorization set and m(G - S) is the order of a maximum component of G - S. The distance majorization integrity of some graphs is obtained. The relations between distance majorization integrity and other parameters are determined. Also a distance majorization integrity of corona of some graphs are computed

참고문헌 (13)

  1. C. A. Barefoot, "Vulnerability in graphs - A comparative survey", J. Combin. Math. Combin. Comput., 1, pp.12~22 (1987)
  2. F. Buckley, "Distance in Graphs" (1990), AddisonWesley
  3. W. Goddard, "Integrity in Graphs: Bounds and Basics", J. Combin. Math. Combin. Comput., 7, pp.139~151 (1990)
  4. F. Harary, "Graph Theory" (1969), Addison Wesley
  5. J. X. Li, "On the second largest laplacian eigenvalues", Linear algebra appl., 438, pp.2438~2446 (2013)
  6. M. J. Morgan, "On the eccentric connectivity index of a graph", Discrete Math., 311, pp.1229~1234 (2011)
  7. Sultan Senan Mahde, "Hub-integrity of graphs", Bulletin of International Mathematical Virtual Institute, 5, pp.57~64 (2015)
  8. Sultan Senan Mahde, "Some operations in hub-integrity of graphs", Asia Pacific Journal of Mathematics, 2, pp.108~123 (2015)
  9. Sultan Senan Mahde, "On the weak hub-integrity of graphs", Gulf journal of mathematics (2017)
  10. Sultan Senan Mahde, "Hub-integrity of line graphs, submitted", ~
  11. Sultan Senan Mahde, "Hub-integrity of splitting graph and dupli-cation of graph element", TWMS J. App. Eng. Math., 6, pp.289~297 (2016)
  12. R. Sundareswaran, "Domination Integrity in Graphs", Proceed-ings of International Conference on Mathematical and Experimental Physics, pp.46~57 (2009)
  13. R. Sundareswaran, "Distance majorization sets in graphs", TWMS J. App. Eng. Math., 5, pp.118~123 (2015)

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