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Degree Associated Reconstruction Number of Split Graphs with Regular Independent Set

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Theoretical Computer Science and Discrete Mathematics (ICTCSDM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10398))

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Abstract

A vertex-deleted subgraph of a graph G with which the degree of the deleted vertex is given is called a degree associated card of G. The degree associated reconstruction number (or drn) of a graph G is the size of the smallest collection of the degree associated cards of G that uniquely determines G. A split graph G is a graph in which the vertices can be partitioned into an independent set and a clique. We prove that the drn is 1 or 2 for all split graphs such that all the vertices in the independent set have equal degree, except four graphs on six vertices and for these exceptional graphs, the drn is 3.

S. Monikandan—Research is supported by the SERB, Govt. of India, Grant no. EMR/2016/000157.

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Acknowledgement

The work reported here is supported by the Research Project EMR/2016/000157 awarded to the second author by SERB, Government of India, New Delhi.

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Authors and Affiliations

  1. Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli, 627 012, India

    N. Kalai Mathi & S. Monikandan

Authors
  1. N. Kalai Mathi
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  2. S. Monikandan
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Correspondence to S. Monikandan .

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Editors and Affiliations

  1. Kalasalingam University, Krishnankoil, India

    S. Arumugam

  2. Ball State University, Muncie, Indiana, USA

    Jay Bagga

  3. Indiana University – Purdue University, Fort Wayne, Indiana, USA

    Lowell W. Beineke

  4. Indian Institute of Technology, New Delhi, India

    B.S. Panda

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Kalai Mathi, N., Monikandan, S. (2017). Degree Associated Reconstruction Number of Split Graphs with Regular Independent Set. In: Arumugam, S., Bagga, J., Beineke, L., Panda, B. (eds) Theoretical Computer Science and Discrete Mathematics. ICTCSDM 2016. Lecture Notes in Computer Science(), vol 10398. Springer, Cham. https://doi.org/10.1007/978-3-319-64419-6_14

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  • DOI: https://doi.org/10.1007/978-3-319-64419-6_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-64418-9

  • Online ISBN: 978-3-319-64419-6

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