Weighted dom-chromatic number of Type-II weighted paths

P. Palanikumar; S. Balamurugan

doi:https://doi.org/10.14445/22315373/IJMTT-V66I5P529

International Journal of Mathematics Trends and Technology

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Volume 66 | Issue 5 | Year 2020 | Article Id. IJMTT-V66I5P529 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I5P529

Weighted dom-chromatic number of Type-II weighted paths

P. Palanikumar, S. Balamurugan

Abstract

A set D of vertices is a dominating set of G if every vertex not in D is adjacent to at least one member of D. A set D of vertices is said to be dom-chromatic if D is a dominating set and X() = X(G). A weighted tree, (T,w) a tree together with a positive weight function on the vertex set w : V(T) ->R+. The weighted domination number γw(T) of (T,w) is the minimum weight w(D) = ΣvεD w(v) of a dominating set D of T. The weighted dom-chromatic number γwch(T) of (T,w) is the minimum weight w(D) = ΣvεD w(v) of a dom-chromatic set D of T. In this paper, we will study the weighted dom-chromatic number of weighted paths. Also, we introduce a new way of weights on the vertices called Type II weighted labeling. We determine the weighted dom-chromatic number of Type II weighted paths.

Keywords

weighted domination, weighted dom-chromatic number, Type-I weighted labeling

References

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Citation :

P. Palanikumar, S. Balamurugan, "Weighted dom-chromatic number of Type-II weighted paths," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 5, pp. 207-218, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I5P529