Quotient-3 Cordial Labeling for Path Related Graphs: Part-II

  • P. Sumathi
  • A. MahalakshmiEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)


A simple graph G(V, E) has order p and size q. Let \(f : V(G) \to {\mathbb Z}_4 - \{0\}\) be a function. For each E(G) define \(f^* : E(G) \to {\mathbb Z}_3\) by \(f^*(uv) = \left \lceil \frac {f(u)}{f(v)} \right \rceil (\text{mod } 3)\) where f(u) ≥ f(v). The function f is said to be quotient-3 cordial labeling if the difference between the number of vertices (edges) labeled with i(k) and the number of vertices (edges) labeled with j(l) by atmost 1. 1 ≤ i, j ≤ 3, i ≠ j, and 0 ≤ k, l ≤ 2, k ≠ l. Here it is proved that some path-related graphs like (Pn;P2), S(Pn;P2), [Pn;Sm] m ≠ 1, S[Pn;S2], Twig(Tgn), and S(Tgn) are quotient-3 cordial.


Star path twig subdivision graph quotient-3 cordial. 



Register our sincere thanks to the referees offered valuable feedback and suggestions.


  1. 1.
    Cahit, I.: Cordial Graphs: A weaker version of Graceful and Harmonious graphs. Ars combin. 23, 201–207 (1987)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Freeda, S, Chellathurai, R.S.: H-1 and H2-cordial labeling of some graphs. Open J. Discrete Math. 2, 149–155 (2012)CrossRefGoogle Scholar
  3. 3.
    Joseph A. Gallian: A Dynamic survey of Graph Labeling. Nineteenth edition, December 23 (2016)Google Scholar
  4. 4.
    Nellai Murugan, A. and Heerajohn, S.: Special Class of Mean Square Cordial Graphs. International Journal of Applied Research. 1(11), 128–131 (2015)Google Scholar
  5. 5.
    Sankar, K. and Sethuraman, G.: Graceful and Cordial labeling of Subdivision of Graphs. Electronic Notes in Discrete Mathematics. 53, 123–131 (2016)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Selvam Avadayappan and Vasuki, R.: New Families of Mean Graphs. International J. Math. Combin., 2, 68–80 (2010)Google Scholar
  7. 7.
    Sumathi, P., Mahalakshmi, A., Rathi, A.: Quotient-3 Cordial Labeling for Star Related Graphs. Global Journal of Pure and Applied Mathematics 13(7), 3909–3918 (2017)Google Scholar
  8. 8.
    Sumathi, P., Mahalakshmi, A., Rathi, A.: Quotient-3 Cordial Labeling for path related graphs part-I. International Journal of Pure and Applied Mathematics 115(9), 249–258 (2017)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsC. Kandaswami Naidu College for MenAnna Nagar, ChennaiIndia
  2. 2.Department of MathematicsSaveetha Engineering CollegeThandalam, ChennaiIndia

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