نبذة مختصرة : We describe a function as – Power 3. If constitute both the induced edge labelling and take be an injective function and express it as, then a graph's Heronian Mean Labelling with p nodes and q lines is or with distinct edge labels. In this manuscript we have proved the – Power -3 Mean labeling behaviour of Path, Twig Graph, Triangular ladder . We have also investigated - Super power -3 Heronian Mean labelling of graghs. Also, we prove that is not – Power - 3 Heronian Mean graph and - Super power -3 Heronian Mean labelling of Snake related graphs like triangular, alternative triangular and double triangular snake graphs.
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