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A graph of order is said to be a prime graph if its vertices can be labeled with the first positive integers in such a way that the labels of any two adjacent vertices in are relatively prime. If such a labeling on exists then it is called a prime labeling. In this paper we seek prime labeling for union of tadpole graphs. We derive a necessary condition for the existence of prime labelings of graphs that are union of tadpole graphs and further show that the condition is also sufficient...
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