Packing Parameters in Graphs

I. Sahul Hamid; S. Saravanakumar

Discussiones Mathematicae Graph Theory (2015)

  • Volume: 35, Issue: 1, page 5-16
  • ISSN: 2083-5892

Abstract

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In a graph G = (V,E), a non-empty set S ⊆ V is said to be an open packing set if no two vertices of S have a common neighbour 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 minimum and maximum cardinalities of a maximal open packing set are respectively called the lower open packing number and the open packing number and are denoted by ρoL and ρo. In this paper, we present some bounds on these parameters.

How to cite

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I. Sahul Hamid, and S. Saravanakumar. "Packing Parameters in Graphs." Discussiones Mathematicae Graph Theory 35.1 (2015): 5-16. <http://eudml.org/doc/271212>.

@article{I2015,
abstract = {In a graph G = (V,E), a non-empty set S ⊆ V is said to be an open packing set if no two vertices of S have a common neighbour 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 minimum and maximum cardinalities of a maximal open packing set are respectively called the lower open packing number and the open packing number and are denoted by ρoL and ρo. In this paper, we present some bounds on these parameters.},
author = {I. Sahul Hamid, S. Saravanakumar},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {packing number; open packing number},
language = {eng},
number = {1},
pages = {5-16},
title = {Packing Parameters in Graphs},
url = {http://eudml.org/doc/271212},
volume = {35},
year = {2015},
}

TY - JOUR
AU - I. Sahul Hamid
AU - S. Saravanakumar
TI - Packing Parameters in Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2015
VL - 35
IS - 1
SP - 5
EP - 16
AB - In a graph G = (V,E), a non-empty set S ⊆ V is said to be an open packing set if no two vertices of S have a common neighbour 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 minimum and maximum cardinalities of a maximal open packing set are respectively called the lower open packing number and the open packing number and are denoted by ρoL and ρo. In this paper, we present some bounds on these parameters.
LA - eng
KW - packing number; open packing number
UR - http://eudml.org/doc/271212
ER -

References

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  1. [1] N. Biggs, Perfect codes in graphs, J. Combin. Theory (B) 15 (1973) 289-296. doi:10.1016/0095-8956(73)90042-7[Crossref] 
  2. [2] G. Chartrand and L. Lesniak, Graphs and Digraphs, Fourth Edition (CRC Press, Boca Raton, 2005). Zbl1057.05001
  3. [3] L. Clark, Perfect domination in random graphs, J. Combin. Math. Combin. Comput. 14 (1993) 173-182. Zbl0793.05106
  4. [4] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1988). Zbl0890.05002
  5. [5] M.A. Henning, Packing in trees, Discrete Math. 186 (1998) 145-155. doi:10.1016/S0012-365X(97)00228-8 [Crossref] 
  6. [6] A. Meir and J.W. Moon, Relations between packing and covering numbers of a tree, Pacific J. Math. 61 (1975) 225-233. doi:10.2140/pjm.1975.61.225[Crossref] Zbl0289.05101
  7. [7] J. Topp and L. Volkmann, On packing and covering number of graphs, Discrete Math. 96 (1991) 229-238. doi:10.1016/0012-365X(91)90316-T [Crossref] Zbl0759.05077

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