Outer independent Roman domination number of trees

Communications in Combinatorics and Optimization

article

Dehgardi, Nasrin¹  Chellali, M² 

[1] Sirjan University of Technology;LAMDA-RO Laboratory, Department of Mathematics University of Blida B.P. 270

关键词: Outer independent Roman dominating function;    outer independent Roman domination number;    tree.;   

DOI  :  10.22049/cco.2021.27072.1191

学科分类：社会科学、人文和艺术（综合）

来源: Azarbaijan Shahide Madani Universit

【 摘 要 】

A Roman dominating function (RDF) on a graph G = (V, E) is a functionf : V → {0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to atleast one vertex v for which f(v) = 2. An RDF f is called an outer independentRoman dominating function (OIRDF) if the set of vertices assigned a 0 under f isan independent set. The weight of an OIRDF is the sum of its function values overall vertices, and the outer independent Roman domination number γoiR(G) is theminimum weight of an OIRDF on G. In this paper, we show that if T is a tree of ordern ≥ 3 with s(T) support vertices, then γoiR(T) ≤ min{5n6,3n+s(T )4}. Moreover, wecharacterize the tress attaining each bound.

【 授权许可】

CC BY-SA