On the Total Irregularity Strength of Fan, Wheel, Triangular Book, and Friendship Graphs

摘要

A totally irregular total k-labeling A : V u E → (1, 2,..., k) of a graph G is a total labeling such that G has a total edge irregular labeling and a total vertex irregular labeling at the same time. The minimum k for which a graph G has a totally irregular total k-labeling is called the total irregularity strength of G, denoted by ts(G). In this paper, we investigate some graphs whose total irregularity strength equals to the lower bound.