Similar d– even vertex odd mean labeling of diverse graphs

Abstract

An injective function F where, F : V(G) → {0,2,4, ..., 2b + 2d - 2} is said to be d-even vertex odd mean labeling (d-EVOML) of the graph G(a, b) when the induced mapping F* : E(G) → {1,3, ..., 2b - 1} given by: F*(lw) = F(l)+F(w)/2, is a bijective function. A d - even vertex odd mean graph is a graph which allows even vertex odd mean labelling. In this study, we identify the lowest value of d for which the graphs: Y-tree, star graph, Px ʘ Kh, crown graph Rh, and rooted product Ph◊C4 have a d- even vertex odd mean labeling. Furthermore, we find the minimum number d for which the graphs: cycle graph Ch when h ≡ 2 mod 4, dragon graph Px(Ch) when h ≡ 2 mod 4, x ≥ 1, prism graph Ph, and Toeplitz graphs Th(1, 3), Th(1, 5) and Th(1, 3, 5) have a similar d- even vertex odd mean labeling. In the end, we establish that no odd cycle Ch is an even vertex odd mean graph for all d.