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 $\Lambda :V\left( G \right) \cup E\left( G \right) \to \left\{ { 1,2,3, \ldots ,\Psi } \right\}$ provided that any two pair of edges have distinct weights is called an edge irregular total $\Psi$-labeling. If $\Psi$ is minimum and $G$ admits an edge irregular total $\Psi$ -labelling, then $\Psi$ is called the total edge irregularity strength (TEIS) and denoted by $\mathrm{tes}\left(G\right).$ In this paper, we start by defining new families of graphs called heptagonal snake graph ${\mathrm{HPS}}_{\mathrm{n}}$,the double heptagonal snake graph $D({\mathrm{HPS}}_{\mathrm{n}}),$ and an $l-$ multiple heptagonal snake graph$L({\mathrm{HPS}}_{\mathrm{n}})$. We follow some steps to deduce the exact value of TEISs for the new families. We first labeled the vertices, and then the edges were labeled such that the weights of edges are different. After that, we calculated that exact value of TEISs for the new families.