### 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) |
---|---|

Pages (from-to) | 160-170 |

Number of pages | 11 |

Journal | Discrete Applied Mathematics |

Volume | 251 |

DOIs | |

State | Published - Dec 31 2018 |

### Fingerprint

### Keywords

- Cactus
- Resistance distance
- Resistance-Harary index

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete Applied Mathematics*,

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

**Maximum Resistance-Harary index of cacti.** / Fang, Wei; Wang, Yi; Liu, Jia Bao; Jing, Guangming.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - Maximum Resistance-Harary index of cacti

AU - Fang, Wei

AU - Wang, Yi

AU - Liu, Jia Bao

AU - Jing, Guangming

PY - 2018/12/31

Y1 - 2018/12/31

N2 - 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].

AB - 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].

KW - Cactus

KW - Resistance distance

KW - Resistance-Harary index

UR - http://www.scopus.com/inward/record.url?scp=85048185882&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048185882&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2018.05.042

DO - 10.1016/j.dam.2018.05.042

M3 - Article

AN - SCOPUS:85048185882

VL - 251

SP - 160

EP - 170

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -