Fuzzy quotient-3 cordial labeling of star related graphs- Paper I

Fuzzy quotient-3 cordial labeling of star related graphs- Paper I

**Authors : **

P. Sumathi ^{1 *} and J. Suresh Kumar ^{2}

**Author Address : **

1 Department of Mathematics, C. Kandaswami Naidu College for Men, Chennai-600102, India.

2 Department of Mathematics, St. Thomas College of Arts and Science, Chennai-600107, India.

*Corresponding author.

**Abstract : **

Let $G(V, E)$ be a simple, finite and planar graph of order $p$ and size $q$. In this paper, the concept of Fuzzy Quotient-3 Cordial Labeling was introduced. Let $sigma : V(G) o [0, 1]$ be a function defined by $sigma(v) = frac{r}{10}$, $r in Z_4 - {0}$. For each edge $uv$ define $mu : E(G) o [0, 1]$ by $mu(uv) = frac{1}{10} lc frac{3sigma(u)}{sigma(v)} c$ where $sigma(u) leq sigma(v)$. The function $sigma$ is called fuzzy quotient-3 cordial labeling of $G$ if the number of vertices labeled with $i$ and the number of vertices labeled with $j$ differ by at most 1, the number of edges labeled with $i$ and the number of edges labeled with $j$ differ by at most 1 where $i, j in left{frac{r}{10}, r in Z_4 - {0} ight}$, $i eq j$. The number of vertices having label $i$ denotes $v_sigma(i)$ and the number of edges having label $i$ denotes $e_mu(i)$. Here it is proved that the Star graph and Star related graphs are Fuzzy Quotient-3 Cordial.

**Keywords : **

Star, Cycle, Fuzzy quotient-3 cordial graph.

**DOI : **

**Article Info : **

*Received : * December 21, 2018; *Accepted : * February 11, 2019.