Interval-valued fuzzy tree (IVFT) and interval-valued fuzzy cycle (IVFC) are defined in this chapter. We characterize interval-valued fuzzy trees. We also prove that if G is an IVFG whose underlying crisp graph is not a tree then G is an IVFT if and only if G contains only ? strong arcs and weak arcs. It is shown that an IVFG G whose underlying crisp graph is a cycle is an IVFC if and only if G has at least two ? strong arcs. 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
Philip A.M.; Kalayathankal S.J.; Kureethara J.V.
Lecture Notes in Networks and Systems, Vol-462, pp. 251-263.
Springer Science and Business Media Deutschland GmbH
Philip A.M., Assumption College, Changanacherry, India; Kalayathankal S.J., Jyothi Engineering College, Thrissur, India; Kureethara J.V., Christ University, Bangalore, India