• CONNECTED ROMAN BLOCK DOMINATION IN GRAPHS
Abstract
A Roman dominating function (RDF) on a block graph B(G) = (H, X) is defined as a function f: H® {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 of B(G) is defined as . The Roman domination number of a block graph B(G) is denoted by , equals the minimum weight of a RDF of B(G). A Roman dominating function of B(G) is connected Roman dominating function of B(G) if either or is connected. The connected Roman block domination number is the minimum weight of a connected Roman block dominating function of B(G). In this paper we establish some results on in terms of elements of G. Further we develop its relationship with other different dominating parameters.
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