A selected tour of the theory of identification matrices

A selected tour of the theory of identification matrices is offered here. We show that shortest-path adjacency matrices are identification matrices for all simple graphs and adjacency matrices are identification matrices for all bipartite graphs. Additionally, we provide an improved proof that augmented adjacency matrices satisfying the circular 1's property are identification matrices. In passing, we present a matrix characterization of doubly convex bipartite graphs. As an application of the theory of identification matrices, we describe an improved method for testing isomorphism of Γ circular arc graphs.

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