Improved upper bounds on the minimum average distance μ(T) of spanning trees T: μ(T) < α + 1 for α ≥ 1, and μ(T) < α + 1/2 + 4(α-1)/α² for α ≥ 7.
Chung, The average distance and the independence number, J
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Generalized expressions for the Wiener index and average distance are obtained for irregular square-cell configurations on the square lattice, treating symmetric families as special cases.
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The average distance of spanning trees in terms of independence number
Improved upper bounds on the minimum average distance μ(T) of spanning trees T: μ(T) < α + 1 for α ≥ 1, and μ(T) < α + 1/2 + 4(α-1)/α² for α ≥ 7.
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Wiener and Average Distance of Irregular Square-Cell Configuration
Generalized expressions for the Wiener index and average distance are obtained for irregular square-cell configurations on the square lattice, treating symmetric families as special cases.