Triangles in inverse NSSD graphs

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.

Keywords:

• NSSD
• graph inverse
• vertex-deleted subgraph
• terminal vertex

AMS Subject Classifications:

• 05C50
• 05C22
• 05C83
• 92E10

Notes

No potential conflict of interest was reported by the authors.