Linear Time Algorithm to Check the Singularity of Block Graphs

  • Ranveer SinghEmail author
  • Naomi Shaked-Monderer
  • Avi Berman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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 



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


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ranveer Singh
    • 1
    Email author
  • Naomi Shaked-Monderer
    • 1
    • 2
  • Avi Berman
    • 1
  1. 1.Technion-Israel Institute of TechnologyHaifaIsrael
  2. 2.The Max Stern Yezreel Valley CollegeYezreel ValleyIsrael

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