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Closed divisor graphs and its labelings

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In this paper, we defined a new graph labelling and named it as closed divisor graph. Let G = (V, E) be a finite undirected (nonempty) graph. A graph G is said to be a closed divisor graph if there exists a vertex labeling using a set S of positive integers, called a quotients of G, such that two vertices are adjacent if and only if one vertex divides the other and their quotient is in the set S. In this paper, we study the properties of closed divisor graph and construct closed divisor labeling for several basic simple graphs and special graphs. We also proved that the closed divisor graph is a generalization of proper monograph. |