Alice A. McRae

In this paper, we initiate the study of a variant of Roman dominating functions. Expand

A dominating set D is a weakly connected dominating set of a connected graph G if (V,E@?(DxV)) is connected. Expand

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

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

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

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

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

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

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

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