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

Let $ G = (V, E) $ be a simple graph with vertex set $ V $ and edge set $ E $, and let $ f $ be a function $ f:V\mapsto \{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...

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Bibliographic Details
Main Authors: Jian Yang, Yuefen Chen, Zhiqiang Li
Format: Article
Language:English
Published: AIMS Press 2023-05-01
Series:AIMS Mathematics
Subjects:
Online Access:https://www.aimspress.com/article/doi/10.3934/math.2023904?viewType=HTML