Semitotal Blocks in Fuzzy Graphs


  • Mohiddin Shaw Narasaraopeta Engineering college, Jawaharlal Nehru Technological University
  • B. Narayana
  • D. Srinivasulu
  • A. Sudhakaraiah


This paper  is a study of  semitotal blocks in fuzzy graphs.  During the study some interesting results regarding the semitotal blocks in fuzzy graphs are obtained.  It is observed that when ‘B’ is a block of a given fuzzy graph                       G:(V, σ, 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                 σ(u), σ(B).  Finally, the result is ∣E STBF(G)∣ = ∣ EF(G)∣ + ∣V(B1)∣ + ∣V(B2)∣ + . . .  + ∣V(Bk)∣.


Author Biography

Mohiddin Shaw, Narasaraopeta Engineering college, Jawaharlal Nehru Technological University

Department of Basic Science and Humanities

Associate Professor


[ 1 ] Arumugam S. and Ramachandran S. "Invitation to Graph Theory", Scitech Publications (India) Pvt. Ltd,

Chennai, (2001).

[ 2 ] Balakrishnan. R and A.Selvam,†k-neighborhood regular graphsâ€, Proceedings of the National

Seminar on Graph Theory, 1996, pp. 35-45.

[ 3 ] Bondy J. A. and Murty U. S. R. "Graph Theory with Applications", The Macmillan Press Ltd, (1976).

[ 4 ] Devadoss Acharya and E.Sampathkumar, “Graphoidal covers and graphoidal covering numbersâ€, Indian J. Pure Appl. Maths., 18(10) (1987), 882-90.

[ 5 ] Frank Harary, Graph Theory, Narosa / Addison Wesley, Indian Student Edition, 1988.

[ 6 ] Kulli V. R. "Minimally Non outer planar Graphs: A survey", (in the Book: “Recent Studies in Graph theory†ed:

V. R. Kulli), Vishwa International Publication, (1989) 177-189.

[ 7 ] Mini To and Sunitha M.S., “On strongest paths, Edges, and Blocks in Fuzzy Graphsâ€, World Applied Sciences

Journal, 22(2013), 10-17.

[ 8 ] NarsingDeo "Graph Theory with Applications to Engineering and Computer Science", Prentice Hall of India

Pvt. Ltd, New Delhi (1997).

[ 9 ] Nagoor Gani. A. and V.T.Chandrasekaran, “A First Look at Fuzzy Graph Theoryâ€, Allied Publishers, 2010.

[ 10 ] Nagoor Gani. A. and K.Radha, On Regular Fuzzy Graphs, Journal of Physical Sciences, Vol. 12, 33 – 40


Rosenfeld . A, in: L.A. Zadeh, K.S.Fu, K.Tanaka and M.Shimura, eds, “Fuzzy sets and their applications to cognitive and decision processâ€, Academic press, New York (1975) 75-95.

Satyanarayana Bh. and Syam Prasad K. "An Isomorphism Theorem on Directed Hypercubes of Dimension n",

Indian J. Pure & Appl. Math 34 (10) (2003) 1453-1457.

Satyanarayana Bh. and Syam Prasad K.. “Discrete Mathematics and Graph Theoryâ€, Prentice Hall of India, New Delhi,


Sunitha M.S., Vijayakumar. A, “ Blocks in Fuzzy Graphsâ€, The journal of fuzzy Mathematics, Vol.13, No.1,





How to Cite

Shaw, M., Narayana, B., Srinivasulu, D., & Sudhakaraiah, A. (2014). Semitotal Blocks in Fuzzy Graphs. Asian Journal of Fuzzy and Applied Mathematics, 2(1). Retrieved from

Most read articles by the same author(s)