In different fields in our life, like physics, coding theory and computer science, graph labeling dramas an vital role and appears in many applications. A labeling of a graph is a map which assign each element in with a positive integer number. An edge irregular total -labeling is a function such that where and are weights for any two distinct edges. In this case, has total edge irregularity strength (TEIS) if is minimum. In our paper, we defined a new type of graphs called a triple star snake graph and star snake graph . Also, we investigated TEIS for a triple star snake graph . After that, we generalized the results for star snake graph .