Chromatic Strong(Weak) Excellent InkmUPn

M Anitha; S Balamurugan

doi:https://doi.org/10.14445/22315373/IJMTT-V53P560

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 53 | Number 6 | Year 2018 | Article Id. IJMTT-V53P560 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P560

Chromatic Strong(Weak) Excellent InkmUPn

M Anitha ,S Balamurugan

Abstract

Let G be an simple undirected graphs. A subset D of V is said to be a chromatic strong(weak) dominating set if D is a strong(weak) dominating set and χ(<D>) = χ (G). The minimum cardinality of a chromatic strong(weak) dominating set in a graph G is called the chromatic strong(weak) dominating number and is denoted by 𝜸 ^𝒄 _𝒔 (G) (𝜸^c_𝒘 (G)).A graph G is called a 𝜸^𝒄_s (𝜸 ^𝒄_𝒘 ) -excellent if every vertex of G belongs to a ^𝜸c_s (𝜸^𝒄_w ) - set. We find that the necessary and sufficient condition for some particular graph, of the form K_mÈP_n, is 𝜸^c_𝒔 - excellent and 𝜸^𝒄_w - excellent.

Keywords

Chromatic strong domination, Chromatic weak domination, Chromatic strong excellent graph, Chromatic weak excellent graph.

References

[1] M.Anitha, S.Balamurugan, A chromatic strong very excellent in caterpillar, International journal of mathematics and soft computing, Submitted.
[2] R. Balakrishnan, K. Ranganathan, A textbook of graph theory, Springer,2011.
[3] S.Balamurugan, G.Prabakaran and V.Swaminathan,On Chromatic Strong Dominating Sets in Graphs, International journal of engineering science, Advanced computing and Bio-Technology, Vol. 2 No. 3, July-Sep 2011, pp 139-149.
[4] J.A.Bondy, U.S.R.Murthy, Graph theory withApplications, North-Holland, 1982.
[5] C.V.R.Harinarayanan, C.Y.Ponnappan, S.P.Subbiah,R.Sundareswaran and V.Swaminathan, Just Excellence and Very Excellence in Graphs with respect to strong domination, Tamkang Journal of Mathematics, Volume 38, Number 2, 167-175, Summer 2007.
[6] T.W.Haynes, Stephen T.Hedetniemi, PeterJ.Slater, Fundamentals of domination in graphs, Marcel dekker, Inc, New york.
[7] T.N.Janakiraman, N.Popalaranjani, Dom chromatic sets of Graphs, International journal of engineering science, Advanced computing and Bio-Technology, Vol. 2 No. 2, Apr-Jun 2011, pp 88-103.
[8] E.Sampathkumar and Pushpalatha, Strong(Weak) domination and domination balance in graph, Discrete Math. 161, (1996), 235-242.
[9] N.Sridharan, M.Yamuna, Very Excellent Graphs and Rigid Very Excellent Graphs, AKCE J. Graphs. Combin., 4, No. 2 (2007), pp. 211-221.

Citation :

M Anitha ,S Balamurugan, "Chromatic Strong(Weak) Excellent InkmUPn," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 6, pp. 496-500, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P560