Characteristic Polynomial of Antiadjacency Matrix of Several Classes of Graph Join

Suppose <em>G</em> is a simple and undirected graph. The adjacency matrix of graph <em>G</em>, denoted by <em>A</em>(<em>G</em>) is a square matrix that representing graph <em>G</em> based on the adjacency of vertices on <em>G</em>, denoted by <em>A</em>(<em>G</em>). The antiadjacency matrix of graph <em>G</em> is a matrix <em>B</em>(<em>G</em>)=<em>J</em>−<em>A</em>(<em>G</em>) where <em>J</em> is an <em>n</em>×<em>n</em> matrixwith all the entries equal to 1. This paper deliver the result of study about the characteristic polynomial of antiadjacency matrix of several graph join, such as multipartite graph, windmill graph, and cone graph.