Czechoslovak Mathematical Journal, Vol. 67, No. 4, pp. 1133-1143, 2017


Unicyclic graphs with bicyclic inverses

Swarup Kumar Panda

Received August 10, 2016.   First published October 12, 2017.

Abstract:  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.
Keywords:  adjacency matrix; unicyclic graph; bicyclic graph; inverse graph; perfect matching
Classification MSC:  05C50, 15A09
DOI:  10.21136/CMJ.2017.0429-16

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Affiliations:   Swarup Kumar Panda, Theoretical Statistics and Mathematics Unit, Indian Statistical Institute Delhi, 7 S.J.S. Sansanwal Marg, New Delhi 110016, India, e-mail: panda.iitg@gmail.com

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