Geodesic
On the zero forcing number of graphs and their splitting graphs
Algebra and discrete mathematics, Tome 28 (2019) no. 1, pp. 29-43

Voir la notice de l'article provenant de la source Math-Net.Ru

In [10], the notion of the splitting graph of a graph was introduced. In this paper we compute the zero forcing number of the splitting graph of a graph and also obtain some bounds besides finding the exact value of this parameter. We prove for any connected graph $\Gamma$ of order $n \ge 2$, $Z[S(\Gamma)]\le 2 Z(\Gamma)$ and also obtain many classes of graph in which $Z[S(\Gamma)]= 2 Z(\Gamma)$. Further, we show some classes of graphs in which $Z[S(\Gamma)] 2 Z(\Gamma)$.
Keywords: zero forcing number, splitting graph, path cover number and domination number of a graph. 
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     author = {Baby Chacko and Charles Dominic and K. P. Premodkumar},
     title = {On the zero forcing number of graphs and their splitting graphs},
     journal = {Algebra and discrete mathematics},
     pages = {29--43},
     publisher = {mathdoc},
     volume = {28},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2019_28_1_a2/}
}
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Baby Chacko; Charles Dominic; K. P. Premodkumar. On the zero forcing number of graphs and their splitting graphs. Algebra and discrete mathematics, Tome 28 (2019) no. 1, pp. 29-43. http://geodesic.mathdoc.fr/item/ADM_2019_28_1_a2/