A note on the open packing number in graphs

Mehdi Mohammadi; Mohammad Maghasedi

Mathematica Bohemica (2019)

  • Volume: 144, Issue: 2, page 221-224
  • ISSN: 0862-7959

Abstract

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A subset S of vertices in a graph G is an open packing set if no pair of vertices of S has a common neighbor in G . An open packing set which is not a proper subset of any open packing set is called a maximal open packing set. The maximum cardinality of an open packing set is called the open packing number and is denoted by ρ o ( G ) . A subset S in a graph G with no isolated vertex is called a total dominating set if any vertex of G is adjacent to some vertex of S . The total domination number of G , denoted by γ t ( G ) , is the minimum cardinality of a total dominating set of G . We characterize graphs of order n and minimium degree at least two with ρ o ( G ) = γ t ( G ) = 1 2 n .

How to cite

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Mohammadi, Mehdi, and Maghasedi, Mohammad. "A note on the open packing number in graphs." Mathematica Bohemica 144.2 (2019): 221-224. <http://eudml.org/doc/294677>.

@article{Mohammadi2019,
abstract = {A subset $S$ of vertices in a graph $G$ is an open packing set if no pair of vertices of $S$ has a common neighbor in $G$. An open packing set which is not a proper subset of any open packing set is called a maximal open packing set. The maximum cardinality of an open packing set is called the open packing number and is denoted by $\rho ^\{\rm o\}(G)$. A subset $S$ in a graph $G$ with no isolated vertex is called a total dominating set if any vertex of $G$ is adjacent to some vertex of $S$. The total domination number of $G$, denoted by $\gamma _t(G)$, is the minimum cardinality of a total dominating set of $G$. We characterize graphs of order $n$ and minimium degree at least two with $\rho ^\{\rm o\}(G)=\gamma _t(G)=\frac\{1\}\{2\}n$.},
author = {Mohammadi, Mehdi, Maghasedi, Mohammad},
journal = {Mathematica Bohemica},
keywords = {packing; open packing; total domination},
language = {eng},
number = {2},
pages = {221-224},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on the open packing number in graphs},
url = {http://eudml.org/doc/294677},
volume = {144},
year = {2019},
}

TY - JOUR
AU - Mohammadi, Mehdi
AU - Maghasedi, Mohammad
TI - A note on the open packing number in graphs
JO - Mathematica Bohemica
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 2
SP - 221
EP - 224
AB - A subset $S$ of vertices in a graph $G$ is an open packing set if no pair of vertices of $S$ has a common neighbor in $G$. An open packing set which is not a proper subset of any open packing set is called a maximal open packing set. The maximum cardinality of an open packing set is called the open packing number and is denoted by $\rho ^{\rm o}(G)$. A subset $S$ in a graph $G$ with no isolated vertex is called a total dominating set if any vertex of $G$ is adjacent to some vertex of $S$. The total domination number of $G$, denoted by $\gamma _t(G)$, is the minimum cardinality of a total dominating set of $G$. We characterize graphs of order $n$ and minimium degree at least two with $\rho ^{\rm o}(G)=\gamma _t(G)=\frac{1}{2}n$.
LA - eng
KW - packing; open packing; total domination
UR - http://eudml.org/doc/294677
ER -

References

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