Further results on even vertex odd mean graphs

Abstract

An even vertex odd mean labeling of an undirected graph with q edges is a one to one function f from the set of vertices V(G) to the set 0, 2, 4, … , 2q such that the induced function f* from E(G) to the set 1, 3, 5, … , 2q – 1 defined by is a bijection. A graph that admits an even vertex odd mean labeling is called even vertex odd mean graph. In this paper, we prove that D₂ (P_n ), D₂ (L_n), D₂ ([P_2n, S_m]), S(L_n), S(P_n ⊗ K₁ ), S(SL_n), S′(P_n), S′(k_2,n), S′(P_n ⊗ K₁ ), S′(C_n) for n ≡ 0 (mod 4) and S′([P_2n, S_m ]) are even vertex odd mean graphs.

Subject Classification:

• 05C78

Keywords:

• Labeling
• Even vertex odd mean labeling
• Even vertex odd mean graphs
• Shadow graph
• Subdivision graph
• Splitting graph