Total Domination Value in Graphs
نویسنده
چکیده
A set D ⊆ V (G) is a total dominating set of G if for every vertex v ∈ V (G) there exists a vertex u ∈ D such that u and v are adjacent. A total dominating set of G of minimum cardinality is called a γt(G)set. For each vertex v ∈ V (G), we define the total domination value of v, TDV (v), to be the number of γt(G)-sets to which v belongs. This definition gives rise to a local study of total domination in graphs. In this paper, we study some basic properties of the TDV function; also, we derive explicit formulas for the TDV of any complete n-partite graph, any cycle, and any path.
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