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A graph is said to be non-singular if it has no eigenvalue equal to zero; otherwise it is singular. Molecular graphs that are non-singular and also have the property that all subgraphs of them obtained by deleting a single vertex are themselves singular, known as NSSD graphs, are of importance in the theory of molecular π-electron conductors; NSSD =… (More)

- Alexander Farrugia
- Discrete Applied Mathematics
- 2016

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)

- Alexander Farrugia, John Baptist Gauci, Irene Sciriha
- Discrete Applied Mathematics
- 2016

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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