A graph = ( , ) with vertices and edges is said to be a Root Square Mean graph if it is possible to label the vertices ∈ with distinct elements ( ) from 1,2, … , + 1 in such a way that when each edge = is labeled with⌋ , then the resulting edge labels are distinct. In this case is called a Root Square Mean labeling of .In this paper we prove that Path ,

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A graph = (,) with vertices and edges is called a Root Square Mean graph if it is possible to label the vertices with distinct labels () from 1,2, … , + 1 in such a way that when each edge = is labeled with (=) = ⌈√ () 2 + () 2 2 ⌉or ⌊√ () 2 + () 2 2 ⌋ , then the edge labels are distinct. In this case is called a Root Square Mean labeling of. In this paper we prove that some disconnected graphs are Root Square Mean graphs.

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