• Publications
  • Influence
Roman {2}-domination
TLDR
In this paper, we initiate the study of a variant of Roman dominating functions. Expand
  • 81
  • 8
On weakly connected domination in graphs
TLDR
A dominating set D is a weakly connected dominating set of a connected graph G if (V,E@?(DxV)) is connected. Expand
  • 67
  • 6
[1, 2]-sets in Graphs
TLDR
A subset S in a graph G=(V,E) is a [j,k]-set if, for every vertex v@?V@?S, j@?|N(v)@? S|@?k for non-negative integers j and k is adjacent to at least j but not more than k vertices in S. Expand
  • 35
  • 4
  • PDF
Minus domination in graphs
TLDR
We introduce one of many classes of problems which can be defined in terms of 3-valued functions on the vertices of a graph G of the form |:V → {−1,0,1}. Expand
  • 49
  • 3
  • PDF
Majority domination in graphs
TLDR
A two-valued function f defined on the vertices of a graph G = (V, E) is a majority dominating function if the sum of its function values over at least half the closed neighborhoods is at least one. Expand
  • 27
  • 3
Self-Stabilizing Algorithms for {k}-Domination
TLDR
In the self-stabilizing algorithmic paradigm for distributed computing each node has only a local view of the system, yet in finite amount of time the system converges to a global state, satisfying some desired property. Expand
  • 12
  • 2
An algorithm for partial Grundy number on trees
TLDR
A coloring of a graph G=(V,E) is a partition {V"1,V2,...,V"k} of V into independent sets or color classes. Expand
  • 17
  • 2
Domination and irredundance in tournaments
TLDR
A set S ⊆ V of vertices in a graph G = (V,E) is called a dominating set if every vertex in V − S is adjacent to at least one vertex in S. Expand
  • 14
  • 2
  • PDF
Independent [1, k]-sets in graphs
TLDR
A subset S ⊆ V in a graph G = (V,E) is a [1, k]-set for a positive integer k if for every vertex v ∈ V \ S, 1 ≤ |N(v) ∩ S| ≤ k, that is, every vertex is adjacent to at least one but not more than k vertices in S. Expand
  • 15
  • 2
  • PDF
Nearly perfect sets in graphs
TLDR
We define n p ( G ) to be the minimum cardinality of a 1-minimal nearly perfect set, and N p (G) to be a maximum cardinality. Expand
  • 14
  • 2