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World Journal of Engineering Research and Technology

( An ISO 9001:2015 Certified International Journal )

An International Peer Reviewed Journal for Engineering Research and Technology

An Official Publication of Society for Advance Healthcare Research (Reg. No. : 01/01/01/31674/16)

ISSN 2454-695X

Impact Factor : 7.029

ICV : 79.45

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Abstract

JUST TOTAL EXCELLENT DOMINATION IN FUZZY GRAPHS

*P. Nithya and K. M. Dharmalingam

ABSTRACT

Let G be a fuzzy graph. A subset D of V is said to be fuzzy dominating set if every vertex u?V(G) there exist there exist a vertex v?V ?D such that uv?E(G) and ?(uv) ?? (u)?? (v) . The minimum cardinality of fuzzy dominating set is denoted by (G) f ? . A Fuzzy graph G is said to be Fuzzy excellent if for every vertex of G belongs to f ? -set of G. In this paper, we introduced a new class of total fuzzy excellent and just total fuzzy excellent (JTFE). Also, in this paper we initiate to study an induced subgraph of a total fuzzy excellent graph and we obtain a necessary and sufficient condition for a graph to be just total fuzzy excellent. We find an upper bound for (G) f t ? . We also prove that every just total fuzzy excellent graph contains no cut vertex.

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