A circulant graph C(n,S) is a graph having its adjacency matrix as a circulant matrix. It can also be intrepreted as a graph with vertices v0,v1,...,vn-1 that are in one to one correspondence with the members of Zn and with edge set {vivj:i-j ∈ S}, where S known as the connection set or symbol, is a subset of non-identity members of Zn that is closed under inverses. This work extends the study of circulant completion and general formulae for calculating circulant completion number in two different perspectives, one in terms of circulant span and the other in terms of adjacency matrix.
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Antony et al. (2024) studied this question.
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