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- Title
圈与圈克罗内克乘积图罗马 {3}-控制.
- Authors
高 红; 黄 佳 欢; 刘 仁 邦; 杨 元 生
- Abstract
Given a graph G=(V, E), f is a function from vertex set V to {0, 1, 2, 3}. If for every vertex v with f(v)=0, the sum of the function values of the vertices in the open neighborhood of v is greater or equal to 3, and for every vertex v with f(v)=1, the sum of the function values of the vertices in the open neighborhood of v is greater or equal to 2, then f is called a Roman {3}-dominating function (R{3}-DF) of graph G. The weight of f, w(f), is the sum of the function values of the vertices all over graph G. The minimum of w(f) is the Roman {3}-domination number of graph G. To determine the Roman {3}-domination number of a graph is an NP complete problem. The upper and lower bounds on the Roman {3} domination numbers of Kronecker product of cycles are presented. The upper bounds are obtained by constructing recursive Roman {3}-dominating functions. The lower bounds are determined based on the result given by others.
- Subjects
DOMINATING set; KRONECKER products; ROMANS
- Publication
Journal of Dalian University of Technology / Dalian Ligong Daxue Xuebao, 2022, Vol 62, Issue 3, p309
- ISSN
1000-8608
- Publication type
Article
- DOI
10.7511/dllgxb202203011