Add to ORKG11 pages, 5 figures, presented at ICGT 2018 The program that led to the results is included in the Source directory (see Other formats) Accepted in DMTCS vol 21. Journal version with their templateInternational audienceWe investigate the 2-domination number for grid graphs, that is the size of a smallest set $D$ of vertices of the grid such that each vertex of the grid belongs to $D$ or has at least two neighbours in $D$. We give a closed formula giving the 2-domination number of any $n \!\times\! m$ grid, hereby confirming the results found by Lu and Xu, and Shaheen et al. for $n \leq 4$ and slightly correct the value of Shaheen et al. for $n = 5$. The proof relies on some dynamic programming algorithms, using transfer matrices in (min,+)-...
Abstract. Roman dominating function of a graph G is a labeling function f: V (G) → {0, 1, 2} such th...
A Roman {2}-dominating function (R2F) is a function f: V → {0, 1, 2} with the property that for ever...
For a graph G=(V,E), a double Roman dominating function is a function f:V→{0,1,2,3} having the prope...
11 pages, 5 figures, presented at ICGT 2018 The program that led to the results is included in the S...
Every graph G = (V, E) has a dominating set S ⊆ V(G) such that any vertex not in S is adjacent to a ...
In combinatorics, a latin square is a n x n matrix filled with n different symbols, each occurring e...
A set S of vertices in a graph G(V,E) is called a total dominating set if every vertex v ∈ V is adja...
: The k \Theta n grid graph is the product P k \Theta P n of a path of length k \Gamma 1 and a path ...
In a Roman domination of a graph, vertices are assigned a value from {0,1,2} in such a way that ever...
In this paper, we initiate the study of a variant of Roman dominating functions. For a graph G=(V,E)...
AbstractA Roman dominating function of a graph G is a function f:V→{0,1,2} such that every vertex wi...
We establish exact values for the $2$-limited broadcast domination number ofvarious grid graphs, in ...
summary:For a graph $G=(V,E)$, a double Roman dominating function is a function $f\colon V\rightarro...
Abstract: Let $$G=(V,E)$$ be a simple graph. A set $$D\subseteq V$$ is a $$2$$-dominating set of $$G...
A Roman dominating function of a graph G is a labeling f: V (G) → {0, 1, 2} such that every vertex ...
Abstract. Roman dominating function of a graph G is a labeling function f: V (G) → {0, 1, 2} such th...
A Roman {2}-dominating function (R2F) is a function f: V → {0, 1, 2} with the property that for ever...
For a graph G=(V,E), a double Roman dominating function is a function f:V→{0,1,2,3} having the prope...
11 pages, 5 figures, presented at ICGT 2018 The program that led to the results is included in the S...
Every graph G = (V, E) has a dominating set S ⊆ V(G) such that any vertex not in S is adjacent to a ...
In combinatorics, a latin square is a n x n matrix filled with n different symbols, each occurring e...
A set S of vertices in a graph G(V,E) is called a total dominating set if every vertex v ∈ V is adja...
: The k \Theta n grid graph is the product P k \Theta P n of a path of length k \Gamma 1 and a path ...
In a Roman domination of a graph, vertices are assigned a value from {0,1,2} in such a way that ever...
In this paper, we initiate the study of a variant of Roman dominating functions. For a graph G=(V,E)...
AbstractA Roman dominating function of a graph G is a function f:V→{0,1,2} such that every vertex wi...
We establish exact values for the $2$-limited broadcast domination number ofvarious grid graphs, in ...
summary:For a graph $G=(V,E)$, a double Roman dominating function is a function $f\colon V\rightarro...
Abstract: Let $$G=(V,E)$$ be a simple graph. A set $$D\subseteq V$$ is a $$2$$-dominating set of $$G...
A Roman dominating function of a graph G is a labeling f: V (G) → {0, 1, 2} such that every vertex ...
Abstract. Roman dominating function of a graph G is a labeling function f: V (G) → {0, 1, 2} such th...
A Roman {2}-dominating function (R2F) is a function f: V → {0, 1, 2} with the property that for ever...
For a graph G=(V,E), a double Roman dominating function is a function f:V→{0,1,2,3} having the prope...