منابع مشابه
Power Domination on Triangular Grids
The concept of power domination emerged from the problem of monitoring electrical systems. Given a graph G and a set S ⊆ V (G), a set M of monitored vertices is built as follows: at first, M contains only the vertices of S and their direct neighbors, and then each time a vertex in M has exactly one neighbor not in M , this neighbor is added to M . The power domination number of a graph G is the...
متن کاملOn the super domination number of graphs
The open neighborhood of a vertex $v$ of a graph $G$ is the set $N(v)$ consisting of all vertices adjacent to $v$ in $G$. For $Dsubseteq V(G)$, we define $overline{D}=V(G)setminus D$. A set $Dsubseteq V(G)$ is called a super dominating set of $G$ if for every vertex $uin overline{D}$, there exists $vin D$ such that $N(v)cap overline{D}={u}$. The super domination number of $G$ is the minimum car...
متن کاملSecure domination and secure total domination in graphs
A secure (total) dominating set of a graph G = (V, E) is a (total) dominating set X ⊆ V with the property that for each u ∈ V − X , there exists x ∈ X adjacent to u such that (X − {x}) ∪ {u} is (total) dominating. The smallest cardinality of a secure (total) dominating set is the secure (total) domination number γs(G) (γst(G)). We characterize graphs with equal total and secure total domination...
متن کاملQuasiperfect domination in triangular lattices
A vertex subset S of a graph G is a perfect (resp. quasiperfect) dominating set in G if each vertex v of G \ S is adjacent to only one vertex (dv ∈ {1, 2} vertices) of S. Perfect and quasiperfect dominating sets in the regular tessellation graph of Schläfli symbol {3, 6} and in its toroidal quotients are investigated, yielding the classification of their perfect dominating sets and most of thei...
متن کاملDomination and Signed Domination Number of Cayley Graphs
In this paper, we investigate domination number as well as signed domination numbers of Cay(G : S) for all cyclic group G of order n, where n in {p^m; pq} and S = { a^i : i in B(1; n)}. We also introduce some families of connected regular graphs gamma such that gamma_S(Gamma) in {2,3,4,5 }.
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ژورنال
عنوان ژورنال: InPrime: Indonesian Journal of Pure and Applied Mathematics
سال: 2020
ISSN: 2716-2478,2686-5335
DOI: 10.15408/inprime.v2i2.15996