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On the trees with maximum Cardinality-Redundance number
Authors: Elham Mohammadi, Nader Jafari Rad
Keywords: Dominating set, Cardinality-Redundance, trees.
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Keywords: Dominating set, Cardinality-Redundance, trees.
Abstract
A vertex $v$ is said to be over-dominated by a set $S$ if $|N[u]\cap S|\geq 2$. The cardinality--redundance of $S$, $CR(S)$, is the number of vertices of $G$ that are over-dominated by $S$. The cardinality--redundance of $G$, $CR(G)$, is the minimum of $CR(S)$ taken over all dominating sets $S$. A dominating set $S$ with $CR(S) = CR(G)$ is called a $CR(G)$-set. In this paper, we prove an upper bound for the cardinality--redundance in trees in terms of the order and the number of leaves, and characterize all trees achieving equality for the proposed bound.Elham Mohammadi1, Nader Jafari Rad2
1;2Department of Mathematics
Shahed University Tehran, Iran
1Elham Mohammadi
E-mail: ,
2Nader Jafari Rad
ORCID: https://orcid.org/0000-0001-7406-1859
E-mail:
1;2Department of Mathematics
Shahed University Tehran, Iran
1Elham Mohammadi
E-mail: ,
2Nader Jafari Rad
ORCID: https://orcid.org/0000-0001-7406-1859
E-mail:
DOI
https://doi.org/10.56415/csjm.v32.03Fulltext
– 0.18 Mb
Contents
- Formal Analysis of Medical Systems using Multi-Agent Systems with Information Sharing
- Outer independent total double Italian domination number
- On the trees with maximum Cardinality-Redundance number
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