Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

ON A VARIANT OF VERTEX EDGE DOMINATION

  • S.V. SIVA RAMA RAJU (Academic Support Department, Abu Dhabi Polytechnic)
  • Received : 2022.08.06
  • Accepted : 2023.04.14
  • Published : 2023.07.30
Download PDF
⟨ Previous Next ⟩

Abstract

A new variant of vertex edge domination, namely semi total vertex edge domination has been introduced in the present paper. A subset S of the vertex set V of a graph G is said to be a semi total vertex edge dominating set(stved - set), if it is a vertex edge dominating set of G and each vertex in S is within a distance two of another vertex in S. An stved-set of G having minimum cardinality is said to be an γstve(G)- set and its cardinality is denoted by γstve(G). Bounds for γstve(G) - set have been given in terms of various graph theoretic parameters and graphs attaining the bounds have been characterized. In particular, bounds for trees have been obtained and extremal trees have been characterized.

Keywords

Acknowledgement

The author would like thank the referee for his valuable suggestions.

References

  1. J.A. Bondy and U.S.R. Murthy, Graph theory with Applications, The Macmillan Press Ltd, New York, 1976.
  2. B. Krishna Kumari, Y.B. Venkata Krishnan, M. Krzywkowski, Bounds on the vertex-edge domination number of a tree, Comptes Rendus Mathematique 352 (2015), 363-366.
  3. E. Delavina, R. Pepper, B. Waller, Lower bounds for the domination number, Discussiones Mathematica Graph Theory 30 (2010), 475-489. https://doi.org/10.7151/dmgt.1508
  4. E.J. Dunbar, J.W. Grossman, J.H. Hattingh, S.T. Hedetneimi, A.A. McRae, On weakly connected domination in graphs, Discrete Mathematics 167 (1997), 261-269. https://doi.org/10.1016/S0012-365X(96)00233-6
  5. I.H. Naga Raja Rao, S.V. Siva Rama Raju, Semi Complete Graphs, International Journal of Computational Cognition 7 (2009), 50-54.
  6. J. Lewis, S.T. Hedetneimi, T. Haynes, G. Fricke, Vertex edge domination, Utilitas Mathematica 81 (2010), 193-213.
  7. J. Peters, Theoretical and algorithmic results on domination and connectivity, Ph.D. Thesis, Clemsen university, 1986.
  8. T. Haynes, S.T. Hedetneimi, P. Slater, Fundamentals of dominations in graphs, Marcel Dekker Inc., New York, Basel, 1998.
  9. W. Goddard, M.A. Henning, Charles A. Mc Pillan, semi total dominations in graphs, Proper citation not available online.