University of TehranJournal of Algorithms and Computation2476-277650120180601One Modulo Three Geometric Mean Graphs1011086834210.22059/jac.2018.68342ENP.JeyanthiGovindammal Aditanar College for Women Tiruchendur-628 215, Tamil Nadu, India.A.MaheswariDepartment of Mathematics Kamaraj College of Engineering and Technology Virudhunagar- 626 001, Tamil Nadu, IndiaP.PandiarajDepartment of Mathematics Kamaraj College of Engineering and Technology Virudhunagar- 626 001, Tamil Nadu, IndiaJournal Article20180128A graph $G$ is said to be one modulo three geometric mean graph if there is an injective function $\phi$ from the vertex set of $G$ to the set $\{a \mid 1\leq a \leq 3q-2\} $ and either $a\equiv 0(mod 3) $ or $ a\equiv 1(mod 3)\}$ where $q$ is the number of edges of $G$ and $\phi$ induces a bijection $\phi^{*}$ form the edge set of $G$ to $\{a \mid 1\leq a\leq 3q-2 $ and $ a\equiv 1(mod3)\}$ given by $\phi^{*}(uv)=\left\lceil \sqrt{\phi(u)\phi(v)}\right\rceil$ or $\left\lfloor \sqrt{\phi(u)\phi(v)}\right\rfloor$ and the function $\phi$ is called one modulo three geometric mean labeling of $G$. In this paper, we establish that some families of graphs admit one modulo three geometric mean labeling.https://jac.ut.ac.ir/article_68342_e53cdfd892a4cf9b99d51c533e8902a6.pdf