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A cyclic wheel graph with order n, where n≥4 can be represented by an anti-adjacency matrix. The anti-adjacency matrix is a square matrix that has entries only 0 and 1. The number 0 denotes there is an edge that connects two vertices, whereas the number 1 denotes otherwise. Every coefficient in characteristic polynomial of the anti-adjacency matrix of a cyclic wheel graph represents the number of induced subgraph that has one or more Hamilton paths minus the number of the cyclic subgraph contained within the induced subgraph. In addition, the eigenvalues can be found through the anti-adjacency matrix of cyclic wheel graph. The result is, the anti-adjacency matrix of cyclic wheel graph has two real eigenvalues and some complex eigenvalues that conjugates to each other. The real eigenvalues are obtained by Horner method, while the complex eigenvalues are obtained by finding the complex roots from the factorization of the characteristic polynomial.

Anti-adjacency; Characteristic Polynomial; Cyclic; Eigenvalue; Induced Graph