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

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 (P _n;P ₂), S(P _n;P ₂), [P _n;S _m] m ≠ 1, S[P _n;S ₂], Twig(Tg _n), and S(Tg _n) are quotient-3 cordial.