Computing total edge irregularity strength for heptagonal snake graph and related graphs

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