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Representation of graphs based on neighborhoods and soft sets

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Abstract

Neighborhood of each vertex in a graph can be very useful in its representation. Soft set theory provides a new tool for such representation. In this paper, a method is being introduced for a graph representation, which is based on adjacency of vertices and soft set theory. With this representation of a graph, application of algebraic operations, available in soft sets may reveal many new aspects of graph theory. In addition, a metric is defined to find distances between graphs represented by soft sets.

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Acknowledgments

This work was partially supported by National Natural Science Foundation of China (Program No. 11301415), Shaanxi Provincial Research Plan for Young Scientific and Technological New Stars (Program No. 2014KJXX-73), Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2013JQ1020), Scientific Research Program Funded by Shaanxi Provincial Education Department of China (Program No. 2013JK1098) and New Star Team of Xi’an University of Posts and Telecommunications.

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Authors and Affiliations

  1. Department of Mathematics, Islamabad Model College for Girls, F-6/2, Islamabad, Pakistan

    Muhammad Irfan Ali

  2. Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

    Muhammad. Shabir

  3. Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an, 710121, China

    Feng Feng

Authors
  1. Muhammad Irfan Ali
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  2. Muhammad. Shabir
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  3. Feng Feng
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Correspondence to Muhammad Irfan Ali.

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Ali, M.I., Shabir, M. & Feng, F. Representation of graphs based on neighborhoods and soft sets. Int. J. Mach. Learn. & Cyber. 8, 1525–1535 (2017). https://doi.org/10.1007/s13042-016-0525-z

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  • DOI: https://doi.org/10.1007/s13042-016-0525-z

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