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

P. Sumathi1^{1} and J. Suresh Kumar^{2}*

^{1}Department of Mathematics, C. Kandaswami Naidu College for Men, Anna Nagar, Chennai 600 102, India

^{2}Department of Mathematics, St. Thomas College of Arts and Science, Koyambedu, Chennai 600 107, India

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 ∈ Z_{4} -{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 v_{σ}(i) and the number of edges
having label i denotes e_{μ}(i) [3]. Here it is proved that Subdivision Star, Subdivision bistar, Splitting graph of star and
bistar are Fuzzy Quotient-3 Cordial.

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

[1] Joseph A. Gallian. A Dynamic survey of Graph Labeling. Nineteenth edition 2016.

[2] Cahit I. Cordial Graphs: A weaker version of Graceful and Harmonious graphs. Arts combin 1987; 23: 201-207.

[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.

[8] Jeyanthi P, Maheswari A. 3-Product Cordial Labeling of Star Graphs. Southeast Asian Bulletin of Mathematics.
2015; 39: 429-437.

[9] Sumathi P, Suresh Kumar J. Fuzzy Quotient-3 cordial labeling of star related graphs-paper I. Malaya Journal of
Matematik 2019; S(1): 79-82.