Prime labeling of line and splitting graph of brush graph

Abstract

A bijective function f from V(G) to {1,2,…, n} be a prime labeling of a graph G with n order if for every u, v ∈ V(G) such that e = uv ∈ E(G), f(u) and f(v) relatively prime. A prime graph is a graph which admits prime labeling. In this study, we investigate and conclude that the line and splitting graph of the brush graph is a prime graph.