TY - JOUR
T1 - Bicyclic Graphs with Unicyclic or Bicyclic Inverses
AU - Wang , Xia
AU - Bian , Hong
AU - Yu , Haizheng
JO - Annals of Applied Mathematics
VL - 3
SP - 270
EP - 281
PY - 2021
DA - 2021/01
SN - 36
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/18592.html
KW - inverse graph, unicyclic graph, bicyclic graph, perfect matching.
AB - <p style="text-align: justify;">A graph $G$ is nonsingular if its adjacency matrix $A(G)$ is nonsingular. A nonsingular graph $G$ is said to have an inverse $G^+$ if $A(G)^{−1}$ is signature similar
to a nonnegative matrix. Let $\mathcal{H}$&nbsp;be the class of connected bipartite graphs with
unique perfect matchings. We present a characterization of bicyclic graphs in
$\mathcal{H}$ which possess unicyclic or bicyclic inverses.</p>