### Abstract

The Resistance-Harary index of a connected graph [Formula presented] is defined as [Formula presented] where [Formula presented] is the resistance distance between vertices [Formula presented] and[Formula presented] in [Formula presented]. A connected graph [Formula presented] is said to be a cactus if each of its blocks is either an edge or a cycle. Let [Formula presented] be the set of all cacti of order [Formula presented] containing exactly [Formula presented] cycles. In this paper, we characterize the graphs with maximum Resistance-Harary index among all graphs in [Formula presented].

Original language | English (US) |
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Pages (from-to) | 160-170 |

Number of pages | 11 |

Journal | Discrete Applied Mathematics |

Volume | 251 |

DOIs | |

State | Published - Dec 31 2018 |

Externally published | Yes |

### Keywords

- Cactus
- Resistance distance
- Resistance-Harary index

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

Fang, W., Wang, Y., Liu, J. B., & Jing, G. (2018). Maximum Resistance-Harary index of cacti.

*Discrete Applied Mathematics*,*251*, 160-170. https://doi.org/10.1016/j.dam.2018.05.042