Strong arcs in fuzzy graphs

  • Authors:

  • Kiran R. Bhutani;Azriel Rosenfeld

  • Affiliations:

  • Department of Mathematics, The Catholic University of America, Washington, DC;Computer Vision Laboratory, Center for Automation Research, University of Maryland, College Park, MD

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2003

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Abstract

An arc of a fuzzy graph is called strong if its weight is at least as great as the strength of connectedness of its end nodes when it is deleted. An arc is strong iff its weight is equal to the strength of connectedness of its end nodes. A bridge is strong, but a strong arc need not be a bridge. An arc of maximum weight is strong, but a strong arc need not have maximum weight. In a connected graph, there is a strong path (a path consisting of strong arcs) between any two nodes. A fuzzy graph is a fuzzy tree iff there is a unique strong path between any two of its nodes. In a fuzzy tree, an arc is strong iff it is a bridge, and a strong path between two nodes is a path of maximum strength between them.