On the Minimum Variable Connectivity Index of Unicyclic Graphs with a Given Order

Shamaila Yousaf, Akhlaq Ahmad Bhatti and Akbar Ali

Discrete Dynamics in Nature and Society, 2020, vol. 2020, 1-9

Abstract:

The variable connectivity index, introduced by the chemist Milan Randić in the first quarter of 1990s, for a graph is defined as , where is a non-negative real number and is the degree of a vertex in . We call this index as the variable Randić index and denote it by . In this paper, we show that the graph created from the star graph of order by adding an edge has the minimum value among all unicyclic graphs of a fixed order , for every and .

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:1217567

DOI: 10.1155/2020/1217567

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