res-lobster

Verrel Rievaldo Wijaya, Lisa Damayanti Ningrum.

Paper link: JMSO

Abstract

Let $G$ be a lobster graph that have three layer of vertices where each layer is connected to each other. The total labeling of the graph is called an edge irregular reflexive $k$-labeling if the total weight of two incident vertices and the edge that joins it is different for all possible edges on the graph. In this paper, we will further discuss the minimum number of $k$ for this kind of labeling on lobster graph. In particular, we determine the exact value of the reflexive edge strength of lobster graph. To help illustrate it, we use Python code to generate the label for the graph.