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Axiomatic Characterization of the Interval Function of a Bipartite Graph

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Book cover Algorithms and Discrete Applied Mathematics (CALDAM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10156))

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Abstract

The axiomatic approach with the interval function and induced path transit function of a connected graph is an interesting topic in metric and related graph theory. In this paper, we introduce a new axiom:

  • (bp) for any \( x,y,z \in V\), \(R(x,y)=\{x,y\} \Rightarrow y\in R(x,z)\) or \(x\in R(y,z)\).

We study axiom (bp) on the interval function and the induced path transit function of a connected, simple and finite graph. We present axiomatic characterizations of the interval function of bipartite graphs and complete bipartite graphs. Further, we present an axiomatic characterization of the induced path transit function of a tree or a 4-cycle.

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Acknowledgments

This research work is supported by NBHM-DAE, Govt. of India under grant No. 2/48(9)/2014/NBHM(R.P)/R & D-II/4364 DATED 17TH NOV, 2014.

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Authors and Affiliations

  1. Department of Futures Studies, University of Kerala, Thiruvananthapuram, India

    Manoj Changat & Ferdoos Hossein Nezhad

  2. Department of Mathematics, IIT Madras, Chennai, India

    Narayanan Narayanan

Authors
  1. Manoj Changat
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  2. Ferdoos Hossein Nezhad
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  3. Narayanan Narayanan
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Corresponding author

Correspondence to Manoj Changat .

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Editors and Affiliations

  1. University of Lethbridge, Lethbridge, Alberta, Canada

    Daya Gaur

  2. Indian Institute of Technology Madras, Chennai, India

    N.S. Narayanaswamy

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Changat, M., Hossein Nezhad, F., Narayanan, N. (2017). Axiomatic Characterization of the Interval Function of a Bipartite Graph. In: Gaur, D., Narayanaswamy, N. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2017. Lecture Notes in Computer Science(), vol 10156. Springer, Cham. https://doi.org/10.1007/978-3-319-53007-9_9

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  • DOI: https://doi.org/10.1007/978-3-319-53007-9_9

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  • Online ISBN: 978-3-319-53007-9

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