Weighted dom-chromatic number of Type-I weighted complete caterpillars

P. Palanikumar; S. Balamurugan

doi:https://doi.org/10.14445/22315373/IJMTT-V66I5P527

International Journal of Mathematics Trends and Technology

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Volume 66 | Issue 5 | Year 2020 | Article Id. IJMTT-V66I5P527 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I5P527

Weighted dom-chromatic number of Type-I weighted complete caterpillars

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. A Caterpillar is a graph which can be obtained from the path on n vertices by appending xi pendant vertices to the ith vertex of the path, Pn. The caterpillar with parameters n,x1,x2,.....,xn will be denoted as Pn(x1,x2,...,xn). In this paper, the weighted dom-chromatic numbers are determined for some Type-I weighted complete caterpillars.

Keywords

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

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Citation :

P. Palanikumar, S. Balamurugan, "Weighted dom-chromatic number of Type-I weighted complete caterpillars," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 5, pp. 195-201, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I5P527