Square Sum Labeling of Octopus Graph and Vanessa Graph: A Brief Mathematical Approach

Abstract

Vanessa graph and Octopus graph admits many labeling such as lucky labeling, square difference labeling, prime labeling, cubic labeling, etc. Inspired by this study, we prove that Octopus graph and Vanessa graph admits one more labeling called square sum labeling. The Octopus graph on and Vanessa graph Vn admit square sum labeling, as this article demonstrated. Vanessa graph is created by joining two fan graphs with a star graph that share a common vertex, and Octopus graph is created by joining a fan graph and a star graph.  In the event that, if f: V (G) \(\to\) {0,1,2, ..., P -1} is odd and prompts infusion action f^*: E(G) \(\to\) N is given by f*(uv) = [f(u)]² + [f(v)]², for all uv \(\in\) E(G).