Open AccessConstruction for trees without domination critical vertices
Author(s) -
Wang Ying,
Fan Wang,
Weisheng Zhao
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021621
Subject(s) - combinatorics , dominating set , mathematics , vertex (graph theory) , domination analysis , graph , discrete mathematics
Denote by $ \gamma(G) $ the domination number of graph $ G $. A vertex $ v $ of a graph $ G $ is called fixed if $ v $ belongs to every minimum dominating set of $ G $, and bad if $ v $ does not belong to any minimum dominating set of $ G $. A vertex $ v $ of $ G $ is called critical if $ \gamma(G-v) < \gamma(G) $. By using these notations of vertices, we give a construction for trees that does not contain critical vertices.