Sandra Mitchell Hedetniemi

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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 χ b (G). In this paper we introduce this coloring and study its properties. In particular, we explore the(More)
A set S is an offensive alliance if for every vertex v in its boundary N (S) − S it holds that the majority of vertices in v's closed neighbourhood are in S. The offensive alliance number is the minimum cardi-nality of an offensive alliance. In this paper we explore the bounds on the offensive alliance and the strong offensive alliance numbers (where a(More)
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)
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) = Σ v∈V f (v). In this paper we introduce and study the minimum and maximum costs of several types of broadcasts in graphs,(More)
ABS'IRACT Two hnear algorithms are presented for solvmg the isomorphism problem for maximal outerplanar graphs (mops) These algorithms present improvements over corresponding hnear algorithms for planar graph isomorphism when apphed to mops The algorithms are based on a code for a mop G which is obtained from a umque Hamdtoman cycle m G The first involves a(More)