Treffer: Total edge irregularity strength for special types of square snake graphs.

One of the extremely useful branches in graph theory is the labeling of a graph. Graph labeling plays a vital role in many fields such as database management, astronomy, coding theory, X-ray crystallography, communication network addressing and radar. A labeling of a connected simple graph G V , E is a map that assign each element in G with a positive integer number. An edge irregular total λ - -labeling is a map β : V G ∪ E G → 1 , 2 , 3 , ... , λ - such that W β h ≠ W β z where W β h and W β z are weights for any two distinct edges. In this case, G has total edge irregularity strength (TEIS) if λ - is minimum. In this paper, a new family of graphs called square snake graphs is defined and denoted by C 4 , n . Moreover, we define some related graphs of square snake graphs named double square snake graph D C 4 , n , triple square snake graph T C 4 , n and m -multiple square snake graph M m C 4 , n . Finally, we determine TEIS for square snake graphs, double square snake graph, triple square snake graph and m -multiple square snake graph, which have many applications in coding theory and physics. [ABSTRACT FROM AUTHOR]