منابع مشابه
On 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 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 }.
متن کاملDomination In The Cross Product Of Digraphs
In many papers, the relation between the domination number of a product of graphs and the product of domination numbers of factors is studied. Here we investigate this problem for domination and total domination numbers in the cross product of digraphs. We give analogues of known results for graphs, and we also present new results for digraphs with sources. Using these results we find dominatio...
متن کاملWhich digraphs are round?
A digraph D is round if the vertices of D can be circularly ordered as VI, V2, ... , Vn so that, for each vertex Vi, the out-neighbours of Vi appear consecutively following Vi and the in-neighbours of Vi appear consecutively preceding Vi in the ordering. We characterize round digraphs in terms of forbidden substructures. Our proof implies a polynomial algorithm to decide if a digraph is round.
متن کاملThe Algorithmic Complexity of Domination Digraphs
Let G = (V,E) be an undirected graph and let π = {V1, V2, . . . , Vk} be a partition of the vertices V of G into k blocks Vi. From this partition one can construct the following digraph D(π) = (π,E(π)), the vertices of which correspond one-to-one with the k blocks Vi of π, and there is an arc from Vi to Vj if every vertex in Vj is adjacent to at least one vertex in Vi, that is, Vi dominates Vj ...
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ژورنال
عنوان ژورنال: Open Mathematics
سال: 2020
ISSN: 2391-5455
DOI: 10.1515/math-2020-0084