On the Harary index of cacti
The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. A connected graph G is a cactus if any two of its cycles have at most one common vertex. Let G(n, r) be the set of cacti of order n and with r cycles, ?(2n,r) the set of cacti of order 2n with a perfect matching and r cycles. In this paper, we give the sharp upper bounds of the Harary index of cacti among G (n,r) and ?(2n, r), respectively, and characterize the corresponding extremal cactus.
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1972 ◽
Vol 15
(3)
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pp. 437-440
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2013 ◽
Vol 7
(1)
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pp. 94-105
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2019 ◽
Vol 16
(1)
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pp. 110-115
2016 ◽
Vol 17
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pp. 10-16
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