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Global Total Roman Domination In Graphs

J. Amjadi, S. Nazari-Moghaddam, S. M. Sheikholeslami
Published 2017 · Mathematics, Computer Science

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A total Roman dominating function (TRDF) on a graph G is a function f : V (G) →{0, 1, 2} satisfying the conditions (i) every vertex u for which f(u) = 0 is adjacent at least one vertex v for which f(v) = 2 and (ii) the subgraph of G induced by the set of all vertices of positive weight has no isolated vertex. The weight of a TRDF is the sum of its function values over all vertices. A total Roman dominating function f is called a global total Roman dominating function (GTRDF) if f is also a TRDF of the complement G¯ of G. The global total Roman domination number of G is the minimum weight of a GTRDF on G. In this paper, we initiate the study of global total Roman domination number and investigate its basic properties. In particular, we relate the global total Roman domination and the total Roman domination and the global Roman domination number.
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