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A Note on Ring Sum of two Fuzzy Graphs

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Author Affiliations

  • 1Department of Basic Sciences and Humanities, Narasaraopeta Engineering College, Narasaraopet, AP, INDIA
  • 2Department of Basic Science and Humanities, NRI Institute of Technology, Vijayawada, AP, INDIA

Res. J. Mathematical & Statistical Sci., Volume 2, Issue (4), Pages 7-9, April,12 (2014)

Abstract

In research paper, it was studied about degree of vertices of a semitotal blocks in fuzzy graphs. In process we obtain some interesting results regarding the degree of the vertices in semitotal blocks in fuzzy graphs. We observed that when ‘B’ is a block of a given fuzzy graph G:(V, s, µ), then degree of the vertex B in semi total block fuzzy graph TSTBF(G) is equal to the sum of the membership grade of the vertices in that block and the number of edges in TSTBF(G) related to block B is ?V(B)? with membership grade minimum of s(u), s(B). Also, we obtained that when G:(V ,s,µ) fuzzy graph and v be a fuzzy vertex with degree dFG(v) in G:(V ,s,µ), then the degree of ‘v’ in semitotal block fuzzy graph TSTBF(G), dSTFG(v) equal to the sum of the degree of the vertex in fuzzy graph and the product of |{B/Bis a block in fuzzy graph containing v}| with minimum of the set { s(v), s(B)}. Finally, it is proved that the ring sum of given fuzzy graph and vertex block fuzzy graph is equals to the semitotal block fuzzy graph of given fuzzy graph.

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