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

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

## Abstract

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.

## Keywords

Star path twig subdivision graph quotient-3 cordial.

## Notes

### Acknowledgement

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

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