Czechoslovak Mathematical Journal, online first, 11 pp.

Unicyclic graphs with bicyclic inverses

Swarup Kumar Panda

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

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

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 2010): 05C50, 15A09

DOI: 10.21136/CMJ.2017.0429-16

Full text available as PDF.


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