Fuzzy quotient-3 cordial labeling on some path related graphs - Paper I

Abstract

In this paper, we discuss the existence of fuzzy quotient-3 cordial labeling on some path related graphs. Let $G(V, E)$ be a simple, finite and planar graph of order $p$ and size $q$. Let $\sigma: V(G) \rightarrow[0,1]$ defined by $\sigma(v)=$ $\frac{r}{10}, r \in Z_4-\{0\}$ and for each $u v \in E(G)$, define $\mu: E(G) \rightarrow[0,1]$ by $\mu(u v)=\frac{1}{10}\left[\frac{3 \sigma(u)}{\sigma(v)}\right\rceil$ where $\sigma(u) \leq \sigma(v)$. When $v_\sigma(i)$ and $v_\sigma(j)$ differ by atmost 1 and $e_\mu(i)$ and $e_\mu(j)$ differ by atmost 1 , the graph $G$ is fuzzy quotient-3 cordial graph. where $v_\sigma(i)$ and $e_\mu(i)$ denotes the number of vertices and edges assigned with $i \in\left\{\frac{\gamma}{10}, \gamma \in Z_4-\{0\}\right\}$.