Total edge irregularity strength for special types of square snake graphs

Abstract

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 Wβ(h) ≠ Wβ(z) where Wβ(h) and Wβ(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 C4,n . Moreover, we define some related graphs of square snake graphs named double square snake graph D(C4,n) , triple square snake graph T(C4,n) and m -multiple square snake graph Mm(C4,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.