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Linear Time Algorithm to Check the Singularity of Block Graphs

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 11394)


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.


  • Block
  • Block graph
  • Nonsingular graph
  • Nullity

AMS Subject Classifications

  • 15A15
  • 05C05

This work is supported by the Joint NSFC-ISF Research Program (jointly funded by the National Natural Science Foundation of China and the Israel Science Foundation (Nos. 11561141001, 2219/15).

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The authors are grateful to Dr. Cheng Zheng for his valuable comments and suggestions.

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Correspondence to Ranveer Singh .

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Singh, R., Shaked-Monderer, N., Berman, A. (2019). Linear Time Algorithm to Check the Singularity of Block Graphs. In: Pal, S., Vijayakumar, A. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2019. Lecture Notes in Computer Science(), vol 11394. Springer, Cham.

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