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Article Content:-
Abstract
The concept of resolving sets and minimum resolving sets has ap-
peared in the name of locating sets and reference sets [6,7]. Indepen-
dently, F. Harary and R.A. Melter discovered these concepts but used
the term metric dimension rather than location number. G. Char-
trand and others introduced the term resolvability in graphs and the
metric dimension in their paper in 2000. Several results have been
found out in resolvability. Equitability was rst introduced in color-
ing by W.Meyer[8]. Degree Equitability in graphs was proposed by E.
Sampathkumar. Later, this concept was used in Domination[2]. An
ordered subset S = {u1; u2; : : : ; uk} of V (G) of a connected graph G
is called a resolving set if the representation of v with respect to S
by (d(v; u1); d(v; u2); : : : ; d(v; uk)) is dierent for dierent v. The min-
imum cardinality of a resolving set in a connected graph G is called
the metric dimension of G and is denoted by dim(G). A resolving set
S is called a complementary equitable resolving set if V
References:-
References
[1] G. Chartrand, L. Eroh, M. Johnson and O.R. Oellermann, Resolvability in graphs and the metric dimension of a graph, Discrete Applied Mathemat- ics, Vol.105, (2000), 99-113.
[2] K.M. Dharmalingam and V. Swaminathan, Degree Equitable Domination in Graphs, Kragujevac Journal of Mathematics, 35(1) (2011), 191-197.
[3] F. Harary and R.A. Melter, On the metric dimension of a graph, Ars Combinatoria, 24 (1976), 191-195.
[4] Hemalatha Subramanian and Subramanian Arasappan, Secure Resolving sets in a graph, Symmetric (Sep, 2018) 1-10.
[5] D. Laksmanaraj, Equitable domination and irredundance in graphs, Ph.D. Thesis, Madurai Kamaraj University (2011).
[6] P.J. Slater, Dominating and reference sets in graphs, J.Math.Phys. Sci.,22 (1988), 445-455.
[7] P.J. Slater, Leaves of trees, Proceedings of sixth South East Conference, Combinatorics Graph Theory and computation, Boca Raton ,14 (1975), 549- 559.
[8] W. Meyer, Equitable Coloring, Amer. Math. Monthly, 80 (1973), 920- 922.