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

摘要

A simple graph G(V, E) has order p and size q. Let f : V(G) →Z_4 - {0} be a function. For each E(G) define f* : E(G) → Z_3 by f*(uv) = {formula} (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.