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Totally connected domination in graphs

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In the last 50 years, Graph theory has seen an explosive growth due to interaction with areas like computer science, electrical and communication engineering, Operations Research etc. Perhaps the fastest growing area within graph theory is the study of domination, the reason being its many and varied applications in such fields as social sciences, communication networks, algorithm designs, computational complexity etc. There are several types of domination depending upon the nature of domination and the nature of the dominating set. In this paper, we introduce the totally connected domination in graphs in connected graphs, exact value for some standard graphs, bounds and some results are established

Abstract

In the last 50 years, Graph theory has seen an explosive growth due to interaction with areas like computer science, electrical and communication engineering, Operations Research etc. Perhaps the fastest growing area within graph theory is the study of domination, the reason being its many and varied applications in such fields as social sciences, communication networks, algorithm designs, computational complexity etc. There are several types of domination depending upon the nature of domination and the nature of the dominating set. In this paper, we introduce the totally connected domination in graphs in connected graphs, exact value for some standard graphs, bounds and some results are established

참고문헌 (14)

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  2. K. D. Dharmalingam, "Studies in Graph Theorey-Equitable domination and bottleneck domination", 박사, pp.2006
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  5. T. W. Haynes, "Fundamentals of domination in graphs" (1998), Marcel Dekker, Inc
  6. S. R. Jayaram, "Line domination in graphs", Graphs Combin, 3, pp.357~363 (1987)
  7. V.R. Kulli, "The non split domination number of a graph", Indian J. pure appl. Math, 27(6), pp.537542~ (1996)
  8. S. Mitchell, "Edge domination in trees", Congr. Numer, 19, pp.489~509 (1977)
  9. E. Sampathkumar, "The neighborhood number of a graph", Indian J. Pure and Appl. Math, 16(2), pp.126~132 (1985)
  10. E. Sampathkumar, "the connected domination number of a graph", J. Math. Phys. Sci, 13, pp.607~613 (1979)
  11. H. B. Walikar, "Recent developmentsin the theory of domination in graphs, Mehta Research instutute, Alahabad", MRI Lecture Notes in Math, 1 (1979)
  12. T. W. Haynes, "Fundamentals of domination in graphs" (1998), Marcel Dekker, Inc
  13. S. M. Hedetneimi, "Disjoint dominating sets in graphs", Proc. Int. Conf. on Disc.Math., IMI-IISc, Bangalore, pp.88~101 (2006)
  14. V. R. Kulli, "Further results on the neighborhood number of a graph", Indian J. Pure and Appl. Math, 23(8), pp.575~577 (1992)

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