# Asia Mathematika

An International Journal. ISSN: 2457-0834 (online)

Volume 3, Issue 2, August 2019, Pages: 53-62

## Fuzzy Quotient-3 Cordial Labeling of Star Related Graphs - Paper II

P. Sumathi11 and J. Suresh Kumar2*

1Department of Mathematics, C. Kandaswami Naidu College for Men, Anna Nagar, Chennai 600 102, India
2Department of Mathematics, St. Thomas College of Arts and Science, Koyambedu, Chennai 600 107, India

### Abstract

Let G be a graph of order p and size q . Let σ : V (G) → [0, 1] be a function defined by σ(v) = r/10, r ∈ Z4 -{0}. For each edge uv define μ : E(G) → [0,1] by μ(uv) = 1/10, where μ(u) ≤ μ(v) . The function σ 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. The number of vertices having label i denotes vσ(i) and the number of edges having label i denotes eμ(i) [3]. Here it is proved that Subdivision Star, Subdivision bistar, Splitting graph of star and bistar are Fuzzy Quotient-3 Cordial.

### Keywords

Subdivision Star, Subdivision bistar, Splitting graph, Fuzzy quotient-3 cordial graph.

### Reference

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[3] Sumathi P, Mahalakshmi A, Rathi A. Quotient-3 Cordial Labeling for Star Related Graphs. Global Journal of Pure and Applied Mathematics 2017; 13(7): 3909-3918.
[4] Sumathi P, Mahalakshmi A, Rathi A. Quotient-3 Cordial Labeling for cycle related graphs. International journal of innovative Research in Applied Sciences and Engineering 2017; 1(2).
[5] Sumathi P, Mahalakshmi A, Rathi A. Quotient-3 Cordial Labeling for path related graphs part-I. International Journal of Pure and Applied Mathematics 2017; 115(9): 249-258.
[6] Sumathi P, Mahalakshmi A, Rathi A. Quotient-3 Cordial Labeling for path related graphs part-II. Communicated on February 2017 and accepted June 2017 ARPN Journal of Engineering and Applied Sciences.
[7] Sumathi P, Mahalakshmi A, Rathi A. Quotient-3 cordial labeling for some Unicyclic graphs-Part-II. International of Journal Innovative Research in Pure and Engineering Mathematics (IJIRPEM) 2017; 1(1): 9-16.
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