Alexander Farrugia

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A universal adjacency matrix U of a graph G is a linear combination of the 0–1 adjacency matrix A, the diagonal matrix of vertex degrees D, the identity matrix I and the matrix J each of whose entries is 1. A main eigenvalue of U is an eigenvalue having an eigenvector that is not orthogonal to the all–ones vector. It is shown that the number of distinct(More)
The n-vertex graph G(= Γ (G)) with a non-singular real symmetric adjacency matrix G, having a zero diagonal and singular (n−1)×(n−1) principal submatrices is termed aNSSD, a Non-Singular graph with a Singular Deck. NSSDs arose in the study of the polynomial reconstruction problem and were later found to characterise non-singular molecular graphs that are(More)
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