Unicyclic graphs with bicyclic inverses

Czechoslovak Mathematical Journal

Swarup Kumar Panda¹ 

关键词: adjacency matrix;    unicyclic graph;    bicyclic graph;    inverse graph;    perfect matching;   

DOI  :  10.21136/CMJ.2017.0429-16

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

  A graph is nonsingular if its adjacency matrix $A(G)$ is nonsingular. The inverse of a nonsingular graph $G$ is a graph whose adjacency matrix is similar to $A(G)^{-1}$ via a particular type of similarity. Let $\mathcal{H}$ denote the class of connected bipartite graphs with unique perfect matchings. Tifenbach and Kirkland (2009) characterized the unicyclic graphs in $\mathcal{H}$ which possess unicyclic inverses. We present a characterization of unicyclic graphs in $\mathcal{H}$ which possess bicyclic inverses.

【 授权许可】

Unknown