Informatics Publishing Limited

A. Nagoorgani ¹, P. Vijayalakshmi ²

Affiliations
1 Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli-620020, Tamilnadu, IN
2 Department of Mathematics, Kundavai Nachiaar Govt. Arts College for women (Autonomous), IN

Abstract

A subset D of V is said to be a fuzzy dominating set of G if for every v V – D, there exists u D such that u dominates v. The minimum cardinality taken over all dominating sets in G is the domination number γ(G). Here the critical arc domination is discussed in the following sense: For each node u, v є D with u and v are not adjacent then γ(G + e) < γ(G) for e = uv an arc between u and v. The existence of such fuzzy graph and it properties are discussed. Finally, insensitive node of fuzzy graph is discussed (i.e) if any node is removed from G then its domination does not change.

Keywords

Critical Arc, Complete Fuzzy Graph, Insensitive Node, Fuzzy Dominating Set, Domination Number Independent Fuzzy Graph, Minimum Dominating Set.

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A. Nagoorgani ¹, A. Mumtaj Begam ²

Affiliations
1 P.G. and Research Department of Mathematics, Jamal Mohamed College, Tamil Nadu, IN
2 Department of Computer Science and Information Technology, Dr. Umayal Ramanathan College for Women, Tamil Nadu, IN

Abstract

This paper introduces a new type of fuzzy shortest path network problem using triangular fuzzy number. To find the smallest edge by the fuzzy distance using graded mean integration representation of generalized fuzzy number for every node. Thus the optimum shortest path for the given problem is obtained.

Keywords

Fuzzy Number, Graded Mean Integration Representation, Fuzzy Distance, Order Relation.

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