文献类型：期刊文献

英文题名：Some sufficient conditions for a tree to have its weak Roman domination number be equal to its domination number plus 1

作者：Yang, Jian[1];Chen, Yuefen[2];Li, Zhiqiang[3]

第一作者：Yang, Jian

通讯作者：Yang, J[1]

机构：[1]Henan Coll Transportat, Dept Publ Basic Teaching, Zhengzhou, Peoples R China;[2]Nanjing Vocat Univ Ind Technol, Dept Publ Basic Courses, Nanjing, Peoples R China;[3]Henan Univ Econ & Law, Sch Math & Informat Sci, Zhengzhou, Peoples R China

第一机构：Henan Coll Transportat, Dept Publ Basic Teaching, Zhengzhou, Peoples R China

通讯机构：[1]corresponding author), Henan Coll Transportat, Dept Publ Basic Teaching, Zhengzhou, Peoples R China.

年份：2023

卷号：8

期号：8

起止页码：17702-17718

外文期刊名：AIMS MATHEMATICS

收录：;Scopus(收录号：2-s2.0-85159890017);WOS:【SCI-EXPANDED(收录号:WOS:000996666900002)】；

基金：Acknowledgments We thank the associate editor and the reviewers for their useful feedback that improved this paper. This work is supported partly by the National Natural Science Foundation (NNSF) of China under Grants 62073122 and 61203050, the Plan of Key Scientific Research Projects of Colleges and Universities in Henan Province (No. 22A880007) , the National Natural Science Foundation of Henan (No. 202300410343) , the Postgraduate Education Reform and Quality Improvement Project of Henan Province (No. YJS2022ZX34) , the Soft Science Research Project of 2023 Science and Technology Development Plan of Henan Province (No. 232400410210) and the Higher Education Teaching Reform research and practice project in Henan Province (No. 2019SJGLX735) .

语种：英文

外文关键词：weak Roman domination number; domination number; tree; star

摘要：Let G = (V, E) be a simple graph with vertex set V and edge set E, and let f be a function f : V 7 -> {0, 1, 2}. A vertex u with f(u) = 0 is said to be undefended with respect to f if it is not adjacent to a vertex with positive weight. The function f is a weak Roman dominating function (WRDF) if each vertex u with f(u) = 0 is adjacent to a vertex v with f (v) > 0 such that the function fu : V 7 -> {0, 1, 2}, defined by fu(u) = 1, fu(v) = f (v) - 1 and fu(w) = f(w) if w is an element of V - {u, v}, has no undefended vertex. The weight of f is w(f) = Zv is an element of V f (v). The weak Roman domination number, denoted gamma r(G), is the minimum weight of a WRDF in G. The domination number, denoted gamma(G), is the minimum cardinality of a dominating set in G. In this paper, we give some sufficient conditions for a tree to have its weak Roman domination number be equal to its domination number plus 1 (gamma r(T) = gamma(T) + 1) by recursion and construction.