On different kinds of arcs in interval valued fuzzy graphs

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Authors :

Ann Mary Philip 1 , Sunny Joseph Kalayathankal 2 and Joseph Varghese Kureethara 3*

Author Address :

1 Department of Mathematics, Assumption College, Mahatma Gandhi University, Changanacherry-686104, India.
2 Department of Mathematics, Kuriakose Elias College, Mahatma Gandhi University, Kottayam-686561, India.
3 Department of Mathematics, CHRIST (Deemed to be University), Bengaluru-560029, India.

*Corresponding author.

Abstract :

Type I strong arcs, Type II strong arcs, left feeble arcs, right feeble arcs and weak arcs in an Interval Valued Fuzzy Graph (IVFG) are introduced in this paper. We obtain a characterization of weak arcs. If every two arcs are comparable in an IVFG, then it contains only $alpha$ strong arcs and weak arcs. An arc in an IVFG is a weak arc if and only if it is the unique weakest arc of at least one cycle in it.

Keywords :

Interval valued fuzzy graph, Arc, Strong arc, Comparable arcs.



Article Info :

Received : December 19, 2018; Accepted : March 09, 2019.



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