ISOLATE DOMINATION OF SOME SPECIAL GRAPHS
Keywords:
domination, isolate domination, cocktail graph, crown graph, gear graph, jump graphAbstract
A dominating set G of S is called an isolate dominating set G of S if the subgraph (S) induced by S has an isolated vertex. In this paper, we investigate the isolate domination of some special graphs such as cocktail party graph, crown graph, gear graph, and jump graph. Characterizations and exact values of isolate domination number were also derived for these graphs.
References
Arriola, B. H. (2015). Isolate Domination in the Join and Corona of Graphs, Applied Mathematical Sciences, 9(31), 1543-1549.
Bacak-Turan, G. and Demirtekin, E. (2017). Neighbor Rupture Degree of Gear Graphs. CBU J. of Sci., 12(2), 319-323.
Biggs, N. L. (1993). Algebraic Graph Theory, 2nd ed. Cambridge, England: Cambridge University Press.
Brandstadt, A., Le, V. and Spinrad, J. (1999). Graph Classes: a survey, SIAM Monographs on Discrete Mathematics and Applications, Springer
Brouwer, E.; Cohen, M.; and Neumaier, A. (1989). Distance-Regular Graphs, New York, Spinger-Verlag.
Harary, F. (1969). Graph Theory, Addison-Wesley Publishing Company, Inc. Philippines Copyright.
Kirlangic, A. (2009). The Rupture Degree and Gear Graphs. Bulletin of the Malaysian Mathematical Sciences Society, 32(1), 31-36.
Kulli, V. R. and Muddebihal, M. H. (2006). The Lict graph and litact graph of a graph, J. of Analysis and Comput., 2(1), 33-43.
Maralabhavi, Y., Anupama, S. and Goudar, V. (2013). Domination Number of Jump Graph. International Mathematical Forum, 8(16), 753-758
Sahul Hamid, I. and Balamurugam, S. (2013), Isolate Domination Number and Maximum Degree, Bulletin of the International Mathematical Virtual Institute, 3, 127-1331.
Bacak-Turan, G. and Demirtekin, E. (2017). Neighbor Rupture Degree of Gear Graphs. CBU J. of Sci., 12(2), 319-323.
Biggs, N. L. (1993). Algebraic Graph Theory, 2nd ed. Cambridge, England: Cambridge University Press.
Brandstadt, A., Le, V. and Spinrad, J. (1999). Graph Classes: a survey, SIAM Monographs on Discrete Mathematics and Applications, Springer
Brouwer, E.; Cohen, M.; and Neumaier, A. (1989). Distance-Regular Graphs, New York, Spinger-Verlag.
Harary, F. (1969). Graph Theory, Addison-Wesley Publishing Company, Inc. Philippines Copyright.
Kirlangic, A. (2009). The Rupture Degree and Gear Graphs. Bulletin of the Malaysian Mathematical Sciences Society, 32(1), 31-36.
Kulli, V. R. and Muddebihal, M. H. (2006). The Lict graph and litact graph of a graph, J. of Analysis and Comput., 2(1), 33-43.
Maralabhavi, Y., Anupama, S. and Goudar, V. (2013). Domination Number of Jump Graph. International Mathematical Forum, 8(16), 753-758
Sahul Hamid, I. and Balamurugam, S. (2013), Isolate Domination Number and Maximum Degree, Bulletin of the International Mathematical Virtual Institute, 3, 127-1331.
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Published
2017-12-22
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