arXiv subjects

Ryan Hessert

Publications and source records attributed to Ryan Hessert.

2 recordsLinked to original sources

arXiv2022

The Inverse of the Incidence Matrix of a Unicyclic Graph

The vertex-edge incidence matrix of a (connected) unicyclic graph G is a square matrix which is invertible if and only if the cycle of G is an odd cycle. A combinatorial formula of the inverse of the incidence matrix of an odd unicyclic graph was known. A combinatorial formula of the Moore-Penrose inverse of the incidence matrix of an even unicyclic graph is presented solving an open problem.

math.CO↗

arXiv2020

Moore-Penrose Inverses of the Signless Laplacian and Edge-Laplacian of Graphs

The signless Laplacian Q and signless edge-Laplacian S of a given graph may or may not be invertible. The Moore-Penrose inverses of Q and S are studied. In particular, using the incidence matrix, we find combinatorial formulas of the Moore- Penrose inverses of Q and S for trees. Also we present combinatorial formulas of the inverses of Q and S for odd unicyclic graphs.

math.CO↗