A matrix characterization of induced paths in bridge graphs
Peter W. Stephens · Linear and Multilinear Algebra · 1994
We present a matrix characterization of induced paths in bridge graphs. This matrix characterization is used to prove the existence of a canonical form for induced paths. Matrices which display this canonical form have only entries of 0,1, and 2. It is then shown that an induced path P=(B 1,B 2,…B q),where Q≥3, can be made into an induced cycle with the addition of a bridge if and only if the canonical form matrices for the path P and the reverse path P R are equivalent and of the form … .