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- Teresa W. Haynes, Sandra Mitchell Hedetniemi, Stephen T. Hedetniemi, Michael A. Henning
- SIAM J. Discrete Math.
- 2002

A function π : V → {1, . . . , k} is a broadcast coloring of order k if π(u) = π(v) implies that the distance between u and v is more than π(u). The minimum order of a broadcast coloring is called the broadcast chromatic number of G, and is denoted χb(G). In this paper we introduce this coloring and study its properties. In particular, we explore the… (More)

- Ashraf M. Abdelbar, Sandra Mitchell Hedetniemi
- Artif. Intell.
- 1998

- Ernest J. Cockayne, Paul A. Dreyer, Sandra Mitchell Hedetniemi, Stephen T. Hedetniemi
- Discrete Mathematics
- 2004

A Roman dominating function on a graph G = (V, E) is a function f : V → {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. The weight of a Roman dominating function is the value f(V ) = ∑ u∈V f(u). The minimum weight of a Roman dominating function on a graph G is called the… (More)

- Terry Beyer, Sandra Mitchell Hedetniemi
- SIAM J. Comput.
- 1980

Consider placing a guard on each vertex of a dominating set S0 of a graph. If for every vertex v / ∈ S0, there is a corresponding guard at an adjacent vertex u for which the resulting set S1 = S0 − {u}∪{v} is dominating, then we say that S0 is 1-secure. It is eternally 1-secure if for any sequence v1, v2, . . . , vk of vertices, there exists a sequence of… (More)

- Sandra Mitchell Hedetniemi, Stephen T. Hedetniemi, Douglas F. Rall
- Discrete Mathematics
- 2000

- Jean E. Dunbar, David J. Erwin, Teresa W. Haynes, Sandra Mitchell Hedetniemi, Stephen T. Hedetniemi
- Discrete Applied Mathematics
- 2006

We say that a function f : V → {0, 1, . . . , diam(G)} is a broadcast if for every vertex v ∈ V , f(v) ≤ e(v), where diam(G) denotes the diameter of G and e(v) denotes the eccentricity of v. The cost of a broadcast is the value f(V ) = Σv∈V f(v). In this paper we introduce and study the minimum and maximum costs of several types of broadcasts in graphs,… (More)

- Sandra Mitchell Hedetniemi
- Inf. Process. Lett.
- 1979