Results 51 to 60 of about 477 (116)

A NOTE ON THE HOP DOMINATION NUMBER OF A SUBDIVISION GRAPH

International Journal of Apllied Mathematics, 2019
Let G = (V,E) be a graph with p vertices and q edges. A subset S ⊂ V (G) is a hop dominating set of G if for every v ∈ V − S, there exists u ∈ S such that d(u, v) = 2. The minimum cardinality of a hop dominating set of G is called a hop domination number
C. Natarajan, S. Ayyaswamy
semanticscholar   +1 more source

Perfect Roman {3}‐Domination in Graphs: Complexity and Bound of Perfect Roman {3}‐Domination Number of Trees

Journal of Mathematics, Volume 2024, Issue 1, 2024.
A perfect Roman {3}‐dominating function on a graph G = (V, E) is a function f : V⟶{0, 1, 2, 3} having the property that if f(v) = 0, then ∑u∈N(v)f(u) = 3, and if f(v) = 1, then ∑u∈N(v)f(u) = 2 for any vertex v ∈ V. The weight of a perfect Roman {3}‐dominating function f is the sum ∑v∈Vf(v).
Ahlam Almulhim, Santi Spadaro
wiley   +1 more source

GLOBAL RAINBOW DOMINATION IN GRAPHS

, 2017
For a positive integer k, a k-rainbow dominating function (kRDF) of a graph G is a function f from the vertex set V.G/ to the set of all subsets of the set f1;2; : : : ;kg such that for any vertex v 2 V.G/ with f .v/ D ¿, the condition S u2N.v/f .u/ D f1;
J. Amjadi, S. Sheikholeslami, L. Volkmann   +2 more
semanticscholar   +1 more source

Total Dominator Chromatic Number on Various Classes of Graphs

International journal of scientific research and reviews, 2019
Let G be a graph with minimum degree at least one. A total dominator coloring of G is a proper coloring of G with the extra property that every vertex in G properly dominates a color class.
Dr.A. Vijayalekshmi, S. Anusha
semanticscholar   +1 more source

1-Movable domination in graphs

, 2014
Let G = (V (G), E(G)) be a connected graph. A non-empty subset S of V (G) is a 1-movable dominating set of G if S is a dominating set of G and for every v ∈ S, S \ {v} is a dominating set of G or there exists a vertex u ∈ (V (G) \ S) ∩ N(v) such that (S \
Renario G. Hinampas, S. Canoy
semanticscholar   +1 more source

1-Movable independent domination in graphs

, 2015
This paper presents some characterizations involving the concept of 1-movable independent domination in graphs and investigates the 1-movable independent dominating sets in the join and corona of graphs.
Renario G. Hinampas, S. Canoy
semanticscholar   +1 more source

Connected Edge Litact Domination in Graphs

International Journal of Innovative Technology and Exploring Engineering, 2019
A subset of edges dominating in is connected edge dominating, if , the subgraph induced by is connected.The connected edge litact domination number , is .In This article we could able to bring up some interesting results on connected edge litact ...

semanticscholar   +1 more source

Blast-Transition Domination for the -∂ Obrazom of Zero Divisor Graph over Ring Zn

International Journal of Engineering and Advanced Technology, 2019
The hub of this article is a search on the behavior of the blast domination and the blast transition domination for the obrazom of zero divisor graphs.AMS Subject Classification: 13A99, 13M99, 05C76, 05C69.

semanticscholar   +1 more source

A Constructive Characterization of Vertex Cover Roman Trees

Discussiones Mathematicae Graph Theory, 2021
A Roman dominating function on a graph G = (V (G), E(G)) is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex u for which f (u) = 0 is adjacent to at least one vertex v for which f (v) = 2.
Martínez Abel Cabrera, Kuziak Dorota, Yero Ismael G.   +2 more
doaj   +1 more source

Isolate domination in the join and corona of graphs

, 2015
A subset S ⊆ V (G) is called an isolate set if the subgraph induced by S has an isolated vertex. This set S is called an isolate dominating set if it is both isolate and dominating.
Benjier H. Arriola
semanticscholar   +1 more source