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Linear Time Algorithm to Check the Singularity of Block Graphs

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Algorithms and Discrete Applied Mathematics (CALDAM 2019)

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

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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.

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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Acknowledgments

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

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Authors and Affiliations

  1. Technion-Israel Institute of Technology, 32000, Haifa, Israel

    Ranveer Singh, Naomi Shaked-Monderer & Avi Berman

  2. The Max Stern Yezreel Valley College, 19300, Yezreel Valley, Israel

    Naomi Shaked-Monderer

Authors
  1. Ranveer Singh
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  2. Naomi Shaked-Monderer
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  3. Avi Berman
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Corresponding author

Correspondence to Ranveer Singh .

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Editors and Affiliations

  1. Indian Institute of Technology, Kharagpur, India

    Sudebkumar Prasant Pal

  2. Cochin University of Science and Technology, Cochin, India

    Ambat Vijayakumar

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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. https://doi.org/10.1007/978-3-030-11509-8_7

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  • DOI: https://doi.org/10.1007/978-3-030-11509-8_7

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  • Print ISBN: 978-3-030-11508-1

  • Online ISBN: 978-3-030-11509-8

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