Minimum Geodetic Fuzzy Subgraph

https://doi.org/10.1016/j.endm.2017.11.039Get rights and content

Abstract

The concept of Minimum geodetic subgraphs in Graph theory was introduced by G. Chartrand, F. Harary and P. Zhang in 2001. In this paper,the idea is extended to fuzzy graphs using geodesic distance.An upper and lower bound for geodesic number of fuzzy graphs is obtained using which it is established that the geodesic number of a fuzzy graph exceeds or is equal to that of its minimum geodetic fuzzy subgraph. A necessary condition for the geodesic number of a fuzzy graph to be 2 depending on the nodes of its minimum geodetic fuzzy subgraph is obtained and a study on the minimum geodetic fuzzy subgraph of a fuzzy tree is conducted.

References (23)

  • G. Chartrand et al.

    On the Geodetic Number of a Graph

    Networks

    (2001)

    • Cited by (1)

    1

    This research was supported by the FDP Grand of University Grants Commission (UGC), New Delhi, India.

    View full text
    © 2017 Elsevier B.V. All rights reserved.