International Journal of Mathematics Trends and Technology
Volume 44 | Number 1 | Year 2017 | Article Id. IJMTT-V44P505 | DOI : https://doi.org/10.14445/22315373/IJMTT-V44P505
A dominating set for a graph G is a subset D of V such that every vertex not in D is adjacent to at least one member of D. This paper deals with some of the graphs having unique minimum dominating sets. We also find a unique minimum dominating sets for block graphs and maximum graphs.
[1] S. Arumugam and S. Ramachandran, Invitation to Graph Theory, Scitech Publications (India) Pvt Ltd,Chennai,2006.
[2] M. Fischermann, L. Volkmann, “Unique minimum domination in trees”, Australas. J. Combin.vol.25, pp.117–124, 2002.
[3] M. Fischermann, L. Volkmann, “Cactus graphs with unique minimum dominating sets”, Utilitas Math., toappear.
[4] M. Fischermann, “Block graphs with unique minimum dominating sets”, Discrete Math., 240, pp. 247–251, 2001.
[5] D.L.Grinstead and P.J.Slater,”On minimum dominating sets with minimum intersection, Discrete Math.86,239-254, 1990.
[6] F.Harary, Graph Theory (Addision Wesley,Reading,Mass, 1969).
[7] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs:Advanced Topics (Marcel Dekker, New York, 1998).
[8] T.W. Haynes, S.T. Hedetniemi, P.J. Slater, “Fundamentals of Domination in Graphs,” Marcel Dekker Inc.New York, 1998.
[9] MirancaFischermann and Lutz Volkmann, Unique minimum domination in trees,Australas. J. Combin.25(2002), 117–124.
[10] NarshingDeo, Graph Theory with Applications to Engineering and Computer Science, PHI Learning Private Limited, New Delhi – 110001,2009.
D.Malarvizhi, V.Revathi, "A Review on Graphs with Unique Minimum Dominating Sets," International Journal of Mathematics Trends and Technology (IJMTT), vol. 44, no. 1, pp. 32-37, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V44P505
PDF 
Abstract 
Keywords 
References 
Citation