Even vertex odd mean labeling of some cycle related graphs

Abstract

Let G be a (p, q) graph and f : V(G) → {0, 2, 4, … , 2q - 2, 2q} be an injection. For each edge e = uv the induced edge labeling f* : E(G) → {1, 3, 5, … , 2q - 1} defined by is a bijection. Then f is called even vertex odd mean labeling if f (V(g)) ∪ { f*(e) : e ∈ E(G)} = {0, 1, 2, 3, … , 2q}. A graph that admits an even vertex odd mean labeling is called even vertex odd mean graph. Here we prove that (C_m; C_n), [C_m; C_n] and are even vertex odd mean graphs for all m, n ≡ 0 (mod 4) and [2P_m; C_n], S_m(C_n) are even vertex odd mean graphs for all m ≥ 1, n ≡ 0 (mod 4).

Subject Classification:

• 05C78

Keywords:

• Labeling
• Even vertex odd mean labeling
• Even vertex odd mean graphs