University of TehranJournal of Algorithms and Computation2476-277650120180601One Modulo Three Geometric Mean Graphs10110868342ENP.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 1leq a leq 3q-2} $ and either $aequiv 0(mod 3) $ or $ aequiv 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 1leq aleq 3q-2 $ and $ aequiv 1(mod3)}$ given by $phi^{*}(uv)=leftlceil sqrt{phi(u)phi(v)}rightrceil$ or $leftlfloor sqrt{phi(u)phi(v)}rightrfloor$ 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