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Inverse of Hermitian Adjacency Matrix of a Mixed Graph |
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PP: 823-828 |
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doi:10.18576/amis/160516
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Author(s) |
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Mohammad Abudayah,
Omar Alomari,
Omar AbuGhneim,
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Abstract |
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| A mixed graph D can be obtained from a graph by orienting some of its edges. Let α be a primitive nth root of unity, then the α−Hermitian adjacency matrix of a mixed graph is defined to be the matrix Hα = [hrs] where hrs = α if rs is an arc in D, hrs = α if sr is an arc in D, hrs = 1 if sr is a digon in D and hrs = 0 otherwise. Accordingly, in this paper we study the invertability of α−hermitian adjacency matrix of a bipartite mixed graph with unique perfect matching. Additionally, we study the inverse of the α−hermitian adjacency matrix of a tree mixed graph with perfect matching. Finally we restrict our study for α = γ the primitive third root of unity where we find that H−1 is {1,−1} diagonally similar to γ−hermitian adjacency matrix of a bipartite graph.
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