International Journal of Mathematics Trends and Technology
Volume 44 | Number 1 | Year 2017 | Article Id. IJMTT-V44P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V44P506
Domination and its variations in graphs are now well studied. However, the original domination number of a graph continues to attract attention. Many bounds have been proven and results obtained for special classes of graphs such as cubic graphs and products of graphs. On the other hand, the decision problem to determine the domination number of a graph remains NP-hard even when restricted to cubic graphs or planar graphs of maximum degree 3. In this paper we consider the domination of planar graphs with small diameter.
[1] G. MacGillivray and K. Seyffarth, Domination numbers of planar graphs. J. Graph Theory 22 (1996), 213–229.
[2] W. McCuaig and B. Shepherd, Domination in graphs with minimum degree two.J. Graph Theory 13 (1989), 749–762.
[3] S.L.Mitchell and S.T.Hedetniemi, Edge domination in trees. Congr. Numer. 19, 489-509, 1977.
[4] M.H.Muddebihal, T.Srinivas and Abdul Majeed, (2012), Domination in block subdivision graphs of graphs, (submitted).
[5] O. Ore, (1962), Theory of graphs, Amer. Math. Soc., Colloq. Publ., 38 Providence.
[6] Pratima panigrahi and S.B.Rao, Graph theory research directions, Narosa publishing house (2011).
[7] E.Sampathkumar and H.B.Walikar, The Connected domination number of a graph, J.Math.Phys. Sci., 13, 607-613,1979.
[8] G.Suresh singh, Graph theory published by K.Ghosh, PHI learning private limited, New Delhi -110001 (2010).
V.Sangeetha, V.Revathi, "A Review on Domination in Planar Graphs with Small Diameter," International Journal of Mathematics Trends and Technology (IJMTT), vol. 44, no. 1, pp. 38-41, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V44P506
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