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.

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Reference

[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.

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