Maximum Resistance-Harary index of cacti

Wei Fang; Yi Wang; Jia Bao Liu; Guangming Jing

doi:10.1016/j.dam.2018.05.042

Maximum Resistance-Harary index of cacti

Wei Fang
, Yi Wang
, Jia Bao Liu
, Guangming Jing

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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	https://doi.org/10.1016/j.dam.2018.05.042
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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10.1016/j.dam.2018.05.042

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title = "Maximum Resistance-Harary index of cacti",

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].",

keywords = "Cactus, Resistance distance, Resistance-Harary index",

author = "Wei Fang and Yi Wang and Liu, \{Jia Bao\} and Guangming Jing",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

year = "2018",

month = dec,

day = "31",

doi = "10.1016/j.dam.2018.05.042",

language = "English (US)",

volume = "251",

pages = "160--170",

journal = "Discrete Applied Mathematics",

issn = "0166-218X",

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}

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 - https://www.scopus.com/pages/publications/85048185882

UR - https://www.scopus.com/pages/publications/85048185882#tab=citedBy

U2 - 10.1016/j.dam.2018.05.042

DO - 10.1016/j.dam.2018.05.042

M3 - Article

AN - SCOPUS:85048185882

SN - 0166-218X

VL - 251

SP - 160

EP - 170

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Maximum Resistance-Harary index of cacti

Abstract

Keywords

ASJC Scopus subject areas

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