Geodesic
Open packing number for some classes of perfect graphs
Ural mathematical journal, Tome 6 (2020) no. 2, pp. 38-43

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Let $G$ be a graph with the vertex set $V(G)$. A subset $S$ of $V(G)$ is an open packing set of $G$ if every pair of vertices in $S$ has no common neighbor in $G.$ The maximum cardinality of an open packing set of $G$ is the open packing number of $G$ and it is denoted by $\rho^o(G)$. In this paper, the exact values of the open packing numbers for some classes of perfect graphs, such as split graphs, $\{P_4, C_4\}$-free graphs, the complement of a bipartite graph, the trestled graph of a perfect graph are obtained.
Keywords: open packing number, 2-packing number, perfect graphs, trestled graphs. 
@article{UMJ_2020_6_2_a3,
     author = {K. Raja Chandrasekar and S. Saravanakumar},
     title = {Open packing number for some classes of perfect graphs},
     journal = {Ural mathematical journal},
     pages = {38--43},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2020_6_2_a3/}
}
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K. Raja Chandrasekar; S. Saravanakumar. Open packing number for some classes of perfect graphs. Ural mathematical journal, Tome 6 (2020) no. 2, pp. 38-43. http://geodesic.mathdoc.fr/item/UMJ_2020_6_2_a3/