Computing Total Edge Irregularity Strength for Heptagonal Snake Graph and Related Graphs

Abstract

A labeling of edges and vertices of a simple graph 𝐺(𝑉,𝐸) by a mapping Ŧ:𝑉(𝐺) ∪ 𝐸(𝐺)→{ 1,2,3,…,Ћ} provided that any two pair of edges have distinct weights is called an edge irregular total Ћ-labeling. If Ћ is minimum and 𝐺 admits an edge irregular total Ћ -labelling, then Ћ is called the total edge irregularity strength (TEIS) and denoted by 𝑡𝑒𝑠(𝐺). In this paper, the definitions of the heptagonal snake graph HPSn ,the double heptagonal snake graph 𝐷(HPSn) and an 𝑙−multiple heptagonal snake graph 𝐿(HPSn) have been introduced. The exact value of TEISs for the new family has also been investigated.