### Abstract

As defined in Chap. 2, a fuzzy graph without fuzzy cutvertices is called a block (nonseparable). Rosenfeld introduced this concept in 1975. In contrast to the classical concept of blocks in graphs, the study of blocks in fuzzy graphs is challenging due to the complexity of cutvertices. Note that cutvertices of a fuzzy graph are those vertices which reduce the strength of connectedness between some pair of vertices on its removal from the fuzzy graph rather than the total disconnection of the fuzzy graph. In this chapter, we concentrate on blocks of fuzzy graphs. This work is from Anjali and Mathew, J Fuzzy Math, 23(4), 907–916 (2015), [28], Anjali and Mathew, J Intell Fuzzy Syst 28, 1659–1665 (2015), [29], Anjali and Mathew, Transitive blocks in fuzzy graphs (2017), [30].

Original language | English (US) |
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Title of host publication | Studies in Fuzziness and Soft Computing |

Publisher | Springer Verlag |

Pages | 127-153 |

Number of pages | 27 |

Volume | 363 |

DOIs | |

State | Published - Jan 1 2018 |

### Publication series

Name | Studies in Fuzziness and Soft Computing |
---|---|

Volume | 363 |

ISSN (Print) | 1434-9922 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Science (miscellaneous)
- Computational Mathematics

### Cite this

*Studies in Fuzziness and Soft Computing*(Vol. 363, pp. 127-153). (Studies in Fuzziness and Soft Computing; Vol. 363). Springer Verlag. https://doi.org/10.1007/978-3-319-71407-3_4

**More on blocks in fuzzy graphs.** / Mathew, Sunil; Mordeson, John N.; Malik, Davender S.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Studies in Fuzziness and Soft Computing.*vol. 363, Studies in Fuzziness and Soft Computing, vol. 363, Springer Verlag, pp. 127-153. https://doi.org/10.1007/978-3-319-71407-3_4

}

TY - CHAP

T1 - More on blocks in fuzzy graphs

AU - Mathew, Sunil

AU - Mordeson, John N.

AU - Malik, Davender S.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - As defined in Chap. 2, a fuzzy graph without fuzzy cutvertices is called a block (nonseparable). Rosenfeld introduced this concept in 1975. In contrast to the classical concept of blocks in graphs, the study of blocks in fuzzy graphs is challenging due to the complexity of cutvertices. Note that cutvertices of a fuzzy graph are those vertices which reduce the strength of connectedness between some pair of vertices on its removal from the fuzzy graph rather than the total disconnection of the fuzzy graph. In this chapter, we concentrate on blocks of fuzzy graphs. This work is from Anjali and Mathew, J Fuzzy Math, 23(4), 907–916 (2015), [28], Anjali and Mathew, J Intell Fuzzy Syst 28, 1659–1665 (2015), [29], Anjali and Mathew, Transitive blocks in fuzzy graphs (2017), [30].

AB - As defined in Chap. 2, a fuzzy graph without fuzzy cutvertices is called a block (nonseparable). Rosenfeld introduced this concept in 1975. In contrast to the classical concept of blocks in graphs, the study of blocks in fuzzy graphs is challenging due to the complexity of cutvertices. Note that cutvertices of a fuzzy graph are those vertices which reduce the strength of connectedness between some pair of vertices on its removal from the fuzzy graph rather than the total disconnection of the fuzzy graph. In this chapter, we concentrate on blocks of fuzzy graphs. This work is from Anjali and Mathew, J Fuzzy Math, 23(4), 907–916 (2015), [28], Anjali and Mathew, J Intell Fuzzy Syst 28, 1659–1665 (2015), [29], Anjali and Mathew, Transitive blocks in fuzzy graphs (2017), [30].

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U2 - 10.1007/978-3-319-71407-3_4

DO - 10.1007/978-3-319-71407-3_4

M3 - Chapter

VL - 363

T3 - Studies in Fuzziness and Soft Computing

SP - 127

EP - 153

BT - Studies in Fuzziness and Soft Computing

PB - Springer Verlag

ER -