Journal of Algorithms and Computation
Open Access

One Modulo Three Geometric Mean Graphs

Document Type : Research Paper

Authors

P. Jeyanthi 1
A. Maheswari 2
P. Pandiaraj 2

1 Govindammal Aditanar College for Women Tiruchendur-628 215, Tamil Nadu, India.

2 Department of Mathematics Kamaraj College of Engineering and Technology Virudhunagar- 626 001, Tamil Nadu, India

https://doi.org/10.22059/jac.2018.68342
Abstract
A 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.

Keywords

mean labeling
one modulo three mean labeling
geometric mean labeling
one modulo three geometric mean labeling
one modulo three geometric mean graph

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