Computing the total edge irregularity strength for quintet snake graph and related graphs

Abstract

In graph theory many useful mathematical disciplines, but the extremely useful one is graph labeling. A graph labeling is used in many applications in various fields like X-ray crystallography, computer science, data base management, coding theory, astronomy and physics. A labeling of edges and vertices of a simple graph G(V, E) by a mapping ¥ : V(G) ∪ E(G) → {1, 2, 3, … , ℜ} provided that any two different edges have distinct weights is called an edge irregular total ℜ -labeling. If ℜ is minimum and G admits an edge irregular total ℜ-labeling, then it is called the total edge irregularity strength (TEIS) denoted by tes(G). In this paper, we have introduced three definitions: the quintet snake graph QS_n , the double quintet snake graph D(QS_n) and the m–multiple quintet snake graph M(QS_n). Moreover, the exact value of TEIS for the new graphs are investigated.

Subject Classification: (2010):

• 05C78

Keywords:

• Irregular labeling
• Total edge irregularity strength
• Edge irregular total labeling
• Quintet snake graph