Abstract
A labeling of a connected, simple and undirected graph G (V, E) is a map that assigns the elements of a graph G with positive numbers. Many types of labeling for graph are found and one of them is a total edge irregularity strength (TEIS) of G, which denoted by tes(G). In the current paper, we defined a new type of family of graph called uniform theta snake graph, On(t, m). Also, the exact values of total edge irregularity strengths for some special types of the new family have been determined.