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Abstract
A nonsingular graph with a singular deck, or NSSD, is an edge-weighted graph with all the diagonal entries of its adjacency matrix and of the inverse
equal to zero. We obtain necessary and sufficient conditions for a two-vertex-deleted subgraph of an NSSD G to remain an NSSD by considering triangles in the inverse NSSD
whose adjacency matrix is
. We also consider the graph obtained by introducing terminal vertices to the NSSD G and show that the conditions for it to be an NSSD are associated with the conditions deduced for the two-vertex deleted subgraph.
Notes
No potential conflict of interest was reported by the authors.