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Total domination number of central graphs
Farshad Kazemnejad,Somayeh Moradi 대한수학회 2019 대한수학회보 Vol.56 No.4
Let $G$ be a graph with no isolated vertex. \emph{A total dominating set}, abbreviated TDS of $G$ is a subset $S$ of vertices of $G$ such that every vertex of $G$ is adjacent to a vertex in $S$. \emph{The total domination number} of $G$ is the minimum cardinality of a TDS of $G$. In this paper, we study the total domination number of central graphs. Indeed, we obtain some tight bounds for the total domination number of a central graph $C(G)$ in terms of some invariants of the graph $G$. Also we characterize the total domination number of the central graph of some families of graphs such as path graphs, cycle graphs, wheel graphs, complete graphs and complete multipartite graphs, explicitly. Moreover, some Nordhaus-Gaddum-like relations are presented for the total domination number of central graphs.
TOTAL DOMINATION NUMBER OF CENTRAL GRAPHS
Kazemnejad, Farshad,Moradi, Somayeh Korean Mathematical Society 2019 대한수학회보 Vol.56 No.4
Let G be a graph with no isolated vertex. A total dominating set, abbreviated TDS of G is a subset S of vertices of G such that every vertex of G is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a TDS of G. In this paper, we study the total domination number of central graphs. Indeed, we obtain some tight bounds for the total domination number of a central graph C(G) in terms of some invariants of the graph G. Also we characterize the total domination number of the central graph of some families of graphs such as path graphs, cycle graphs, wheel graphs, complete graphs and complete multipartite graphs, explicitly. Moreover, some Nordhaus-Gaddum-like relations are presented for the total domination number of central graphs.