Volume 31 | Number 2 | Year 2016 | Article Id. IJMTT-V31P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V31P512

Let G (V, E) be a simple, finite and undirected connected graph. A nonempty set S V of a graph G is a dominating set, if every vertex in V – S is adjacent to atleast one vertex in S. A dominating set S V is called a locating dominating set, if for any two vertices v, w V – S, N(v) S N(w) S. A locating dominating set S V is called a co – isolated locating dominating set (cild – set), if there exists atleast one isolated vertex in . The domination number (G) of a graph G is the minimum cardinality of a dominating set. The locating domination number ld(G) and co – isolated locating domination number cild(G) are defined in the same way. A partition of V(G), all of whose classes are cild – sets in G is called a co – isolated locating domatic partition of G. The maximum number of classes of a co – isolated locating domatic partition of G is called the co – isolated locating domatic number of G and denoted by dcild(G). In this paper, connected graphs satisfying the relation cild(G) ld(G) (G) are constructed. Also the bounds for dcild(G) are obtained.

[1] N. Bertrand, I. Charon, O. Hudry, A. Lobstein, Identifying And Locating – Dominating Codes on Chains And Cycles, European Journal Of Combinatorics, Vol. 25, No.7(2004), p. 969 – 987.

[2] M. Chellai, M. Mimouni and P.J. Slater, On Locatingdomination in graphs, Discuss. Math. Graph Theory, Vol. 30 (2010), p. 223 – 235.

[3] E.J. Cockayne, S.T. Hedetniemi, Towards A Theory Of Domination In Graphs, Networks 7,1997, p. 247 – 261.

[4] F. Harary, Graph Theory, Addison – Wesley, Reading Mass, 1969.

[5] T.W. Haynes, S.T. Hedetniemi, P.J. Slater, Fundamental Of Domination In Graphs, Marcel Dekker, New York, 1997.

[6] V.R. Kulli, Theory of Domination in Graphs, Vishwa International Publications, 2010.

[7] S. Muthammai, N. Meenal, Co - isolated Locating Domination Number for some standard Graphs, National conference on Applications of Mathematics & Computer Science (NCAMCS-2012), S.D.N.B Vaishnav College for Women(Autonomous), Chennai, February 10, 2012, p. 60 – 61.

[8] S. Muthammai, N. Meenal, Co - isolated Locating Domination Number of a Graph, Proceedings of the UGC sponsored National Seminar on Applications in Graph Theory, Seethalakshmi Ramaswamy College(Autonomous), Tiruchirappalli, 18th & 19th December 2012, p. 7 – 9.

[9] S. Muthammai, N. Meenal, Co – isolated Locating Domination Number For The Complement Of a Doubly Connected Graph., International Journal of Mathematics And Scientific Computing, Vol. 5, No. 1, 2015, p.57 – 59, ISSN: 2231 – 5330.

[10] S. Muthammai, N. Meenal, Co – Isolated Locating Dominating Number For Cubic Graphs, International Conference on Mathematical Computer Engineering(ICMCE – 2015), Organized by the School of Advanced Sciences, VIT University, Chennai, 14 – 15, December 2015.

[11] O. Ore, Theory of Graphs, Amer. Math. Soc. Coel. Publ. 38, Providence, RI, 1962.

[12] D.F. Rall, P. J. Slater, On location domination number for certain classes of graphs, Congrences Numerantium, 45 (1984), p. 77 – 106.

[13] B. Zelinka, Location – Domatic Number Of A Graph, Mathematica Bohemica, Vol. 123(1998), No. 1, p. 67 – 71.

S. Muthammai, N. Meenal, "More Results on Co – Isolated Locating Domination Number of Graphs," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 31, no. 2, pp. 46-52, 2016. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V31P512