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- W2007604426 abstract "Let G ( k , n ) be the set of connected simple n -vertex graphs with minimum vertex degree k . The Randić index R ( G ) of a graph G is defined by R ( G ) = ∑ u v ∈ E ( G ) 1 d ( u ) d ( v ) , where d ( u ) is the degree of vertex u and the summation extends over all edges u v of G . In this paper we prove for k ≥ n 2 the conjecture of Aouchiche and Hansen about the graphs in G ( k , n ) for which the Randić index attains its minimum value. We show that the extremal graphs have only two degrees ( k and n − 1 ), and the number of vertices of degree k is as close to n 2 as possible. At the end we state the solutions of the more detailed optimization problems over graphs with arbitrary maximum vertex degree m , except in the case when k , m and n are odd numbers." @default.
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- W2007604426 date "2013-02-01" @default.
- W2007604426 modified "2023-09-29" @default.
- W2007604426 title "On the conjecture of Aouchiche and Hansen about the Randić index" @default.
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- W2007604426 doi "https://doi.org/10.1016/j.disc.2012.10.012" @default.
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