Total Mean Cordiality of Umbrella, Butterfly and Dumbbell Graphs

Abstract

A Total Mean Cordial labeling of a graph G = (V,E) is a function f : V (G) →{0. 1. 2} such that for each edge xy assign the label [(f(x)+f(y))/2] where x, y ∈ V (G) and |ev_f (i) -ev_f (j)| ≤ 1, i, j ∈ {0. 1. 2} where ev_f (x) denotes the total number of vertices and edges labeled with x (x = 0, 1, 2). If there exists a total mean cordial labeling on a graph G, we will call G is Total Mean Cordial. In this paper, we investigate the Total Mean Cordial labeling behavior of fan, umbrella, dumbbell, and buttery graphs.

Key words and phrases. path, join of graphs, fan, complete graph, cycle.

1991 Mathematics Subject Classification. 05C78