Maximum Resistance-Harary index of cacti

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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)160-170
Number of pages11
JournalDiscrete Applied Mathematics
Volume251
DOIs
StatePublished - Dec 31 2018

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Cactus
Connected graph
Resistance
Cycle
Graph in graph theory

Keywords

  • Cactus
  • Resistance distance
  • Resistance-Harary index

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

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

In: Discrete Applied Mathematics, Vol. 251, 31.12.2018, p. 160-170.

Research output: Contribution to journalArticle

Fang, Wei ; Wang, Yi ; Liu, Jia Bao ; Jing, Guangming. / Maximum Resistance-Harary index of cacti. In: Discrete Applied Mathematics. 2018 ; Vol. 251. pp. 160-170.
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