Abstract :
This paper studies singular graphs by considering minimal singular induced subgraphs of small order. These correspond to a number k of linearly dependent rows of the adjacency matrix determining what is termed as a core of the singular graph. For k at most 5, the distinct cores and corresponding minimal configurations (61 in number) are identified. This provides a method of constructing singular graphs from others of smaller order. Furthermore, it is shown that when a graph has a minimal configuration as an induced subgraph, then it is singular.
