A way to construct independence equivalent graphs

Abstract

Let us denote the independence polynomial of a graph by I G ( x ) . If I G ( x ) = I H ( x ) implies that G ≅ H then we say G is independence unique . For graph G and H if I G ( x ) = I H ( x ) but G and H are not isomorphic, then we say G and H are independence equivalent . In [7] , Brown and Hoshino gave a way to construct independent equivalent graphs for circulant graphs . In this work we give a way to construct the independence equivalent graphs for general simple graphs and obtain some properties of the independence polynomial of paths and cycles .