Results 101 to 110 of about 1,516 (111)

Trees with the same distance domination number

, 2020
The distance between two vertices u and v in a graph G equals the length of a shortest path from u to v. A set D of vertices is distance-k dominating if every vertex not belonging to D is at distance at most k of a vertex in D.
Min-Jen Jou, Jenq-Jong Lin, Qian-Yu Lin
semanticscholar   +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

The 3-independence number of trees

, 2020
The 3-independence number of a graph G, denoted by α3(G), is the maximum size of a set of vertices at pairwise distance greater than three. Here we focus on the trees.
Jenq-Jong Lin, Min-Jen Jou, Qian-Yu Lin
semanticscholar   +1 more source

Secure domination in the joins of graphs

, 2014
In this paper, we revisited the concept of secure dominating set introduced by Cockayne et al. We characterized secure dominating set in terms of the concept of external private neighborhood of a vertex.
Elmer Castillano, Rose Ann L. Ugbinada, S. Canoy   +2 more
semanticscholar   +1 more source

On the 2-independence number of connected graphs

, 2020
The distance between two vertices u and v in a graph G equals the length of a shortest path from u to v. A set S of vertices is a 2independent set if the distance between any two elements in S is greater than two in G.
Min-Jen Jou, Jenq-Jong Lin, Qian-Yu Lin
semanticscholar   +1 more source

Secure convex dominating sets in corona of graphs

, 2015
In this paper, we characterize the secure convex dominating sets in the corona of two connected graphs and then determine the corresponding secure convex domination numbers of these graphs.
Enrico L. Enriquez
semanticscholar   +1 more source

Clique domination in a graph

, 2015
Let G be a nontrivial connected graph. A nonempty subset S of V (G) is a clique dominating set of G if S is a dominating set and the induced subgraph 〈S〉 of S is complete.
T. V. Daniel, S. Canoy
semanticscholar   +1 more source

Secure convex dominating sets in products of graphs

, 2015
In this paper, we characterize the secure convex dominating sets in the lexicographic and Cartesian products of two connected graphs and then determine the corresponding secure convex domination numbers of these graphs. Mathematics Subject Classification:
Enrico L. Enriquez, S. Canoy
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 total dominating, connected dominating, and double dominating sets in the composition of graphs

, 2015
This study aimed to characterize 1-movable total dominating sets and 1-movable connected dominating sets in the composition G[H] of arbitrary connected nontrivial graphs G and H and determine the corresponding value of the parameters.
Jocecar Lomarda, S. Canoy
semanticscholar   +1 more source