### Geometric mean cordial labeling of graphs

#### Abstract

Let $G =(V,E)$ be a graph and $f$ be a mapping from $V(G) \rightarrow \left\{0,1,2 \right\}$. For each edge $uv$ assign the label \(\left\lceil\sqrt{f(u)f(v)}\right\rceil\), $f$ is called a geometric mean cordial labeling if $\mid v_f (i)- v_f (j)\mid \leq 1 $ and $\mid e_f (i)- e_f (j) \mid \leq1 $, where $v_f(x)$ and $e_f(x)$ denote the number of vertices and edges labeled with $x$, $x \in\left\{ 0,1,2 \right\}$ respectively. A graph with a geometric mean cordial labeling is called geometric mean cordial graph. In this paper geometric mean cordiality of some standard graphs such as path, star, cycle, complete graph, complete bipartite graph, wheel are discussed.

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