Merger and Vertex Splitting in Divisor Graphs
نویسندگان
چکیده
In this paper, we study some operations which produce new divisor graphs from old ones. We prove that the contraction of a divisor graph along a bridge is a divisor graph. For two transmitters (receivers) u and v in some divisor orientation of a divisor graph G, it is shown that the merger G |u,v is also a divisor graph. Two special types of vertex splitting are introduced, one of which produces a divisor graph when applied on a cutvertex of a given divisor graph, while the other is applied on a transmitter (receiver) in some divisor orientation of a given divisor graph and produces a divisor graph. Mathematics Subject Classification: 05C20, 05C78
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