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| BICYCLIC GRAPHS WITH UNICYCLIC OR BICYCLIC INVERSES |
| Xia Wang,Hong Bian,Haizheng Yu |
| (School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830054, Xinjiang, PR China;College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, Xinjiang, PR China) |
| DOI： |
| Abstract: |
| 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 $\mathcal{H}$ 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. |
| Key words: inverse graph; unicyclic graph; bicyclic graph; perfect matching |