Further results on independent double roman trees. Issue 3 (2nd September 2022)

• Record Type: Journal Article
• Authors: Rahmouni, A.; Abdollahzadeh Ahangar, H.; Chellali, M.; Sheikholeslami, S. M.
• Is Part Of: AKCE International Journal of Graphs and Combinatorics. Volume 19:Issue 3(2022)
• Page Start: 311
• Page End: 315
• Publication Date: 2022-09-02
• Subjects: Independent double Roman domination -- independent domination -- trees; 05C69 -- 05C05
• DOI: 10.1080/09728600.2022.2148140
• Languages: English
• ISSNs: 0972-8600

Abstract

Abstract: A double Roman dominating function (DRDF) on a graph G = ( V, E ) is a function f : V → { 0, 1, 2, 3 } such that every vertex u with f ( u ) = 0 is adjacent to at least one vertex assigned a 3 or to at least two vertices assigned a 2, and every vertex v with f ( v ) = 1 is adjacent to at least one vertex assigned 2 or 3. The weight of a DRDF is the sum of its function values over all vertices. A DRDF f is an independent double Roman dominating function (IDRDF) if the set of vertices assigned 1, 2 and 3 is independent. The independent double Roman domination number i d R ( G ), is the minimum weight over all IDRDFs of G . Every graph G satisfies i d R ( G ) ≤ 3 i ( G ), where i ( G ) is the independent domination number. In this paper, we give a characterization of all trees T with i d R ( T ) = 3 i ( T ) .