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The Cartographer
Linear time algorithm to check the singularity of block graphs
August 10, 2018 Β· Declared Dead Β· π International Conference on Algorithms and Discrete Applied Mathematics
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Authors
Ranveer Singh, Naomi Shaked-Monderer, Avi Berman
arXiv ID
1808.03411
Category
cs.DS: Data Structures & Algorithms
Citations
2
Venue
International Conference on Algorithms and Discrete Applied Mathematics
Last Checked
4 months ago
Abstract
A block graph is a graph in which every block is a complete graph. Let $G$ be a block graph and let $A(G)$ be its (0,1)-adjacency matrix. Graph $G$ is called nonsingular (singular) if $A(G)$ is nonsingular (singular). Characterizing nonsingular block graphs is an interesting open problem proposed by Bapat and Roy in 2013. In this article, we give a linear time algorithm to check whether a given block graph is singular or not.
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