Unicyclic graphs with bicyclic inverses

Swarup Kumar Panda

Czechoslovak Mathematical Journal (2017)

  • Volume: 67, Issue: 4, page 1133-1143
  • ISSN: 0011-4642

Abstract

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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 ℋ denote the class of connected bipartite graphs with unique perfect matchings. Tifenbach and Kirkland (2009) characterized the unicyclic graphs in ℋ which possess unicyclic inverses. We present a characterization of unicyclic graphs in ℋ which possess bicyclic inverses.

How to cite

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Panda, Swarup Kumar. "Unicyclic graphs with bicyclic inverses." Czechoslovak Mathematical Journal 67.4 (2017): 1133-1143. <http://eudml.org/doc/294230>.

@article{Panda2017,
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.},
author = {Panda, Swarup Kumar},
journal = {Czechoslovak Mathematical Journal},
keywords = {adjacency matrix; unicyclic graph; bicyclic graph; inverse graph; perfect matching},
language = {eng},
number = {4},
pages = {1133-1143},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Unicyclic graphs with bicyclic inverses},
url = {http://eudml.org/doc/294230},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Panda, Swarup Kumar
TI - Unicyclic graphs with bicyclic inverses
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 4
SP - 1133
EP - 1143
AB - 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.
LA - eng
KW - adjacency matrix; unicyclic graph; bicyclic graph; inverse graph; perfect matching
UR - http://eudml.org/doc/294230
ER -

References

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