One Modulo Three Root Square Mean Labeling of Some Disconnected Graphs

Abstract

A graph G is said to be one modulo three root square mean graph if there is an injective function φ from the vertex set of G to the set {0, 1, 3, …, 3q-2, 3q} where q is the number of edges of G and φ induces a bijection φ* from the edge set of G to{1, 4, …, 3q-2} given by φ*(uv) = ቜට ሾఝሺ௨ሻሿ మ ାሾఝሺ௩ሻሿ మ ଶ ቝ or ට ሾఝሺ௨ሻሿ మ ାሾఝሺ௩ሻሿ మ ଶ and the function φ is called one modulo three root square mean labeling of G. The concept of one modulo three root square mean labeling was introduced by Jayasekaran and Jaslin Melbha and they investigated some graphs are one modulo three root square mean graphs. In this paper we prove that some disconnected graphs are one modulo three root square mean labeling.