Analytic Mean Labeling in Certain Classes of Graphs

Resumo

A graph labeling is a mapping, when the map assigns integers to vertices/edges, it is called
vertex/edge labeling and when it assigns to both, it is called total labeling. The idea of mean labeling was
proposed by Somasundaram and Ponraj. An injective function f : V → {t : 0 ≤ t ≤ q} is called a mean
labeling of a graph G(V,E) if for every u, v ∈ V , the edge labels are (f(u)+f(v))/2 whenever f(u) + f(v) is even and (f(u)+f(v)+1)/2 whenever f(u) + f(v) is odd such that edge labels are distinct. The idea of analytic mean
labeling was coined by Tharmaraj and Sarasija and they have proved the existence in the following graphs:
path,cycle, star, Ladder, bistar, fan, comb and the joint sum of two copies of certain graph. The concept
of Analytic even mean labeling is introduced by Sajitha Kumari et., al, and they proved Jewel graph, Jelly
Fish graph, Triangular Book graph, Triangular Book with Book Mark admits analytic even mean labeling.
Motivated by these studies, here we examine the existence of Analytic Mean labeling and Analytic Even Mean
Labeling in the duplicate graphs of ladder, triangular ladder, slant ladder and Zig-Zag ladder graphs.