ON THE TOTAL DISTANCE AND DIAMETER OF GRAPHS
2018 ◽
Vol 98
(1)
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pp. 14-17
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The total distance (or Wiener index) of a connected graph$G$is the sum of all distances between unordered pairs of vertices of$G$. DeLaViña and Waller [‘Spanning trees with many leaves and average distance’,Electron. J. Combin.15(1) (2008), R33, 14 pp.] conjectured in 2008 that if$G$has diameter$D>2$and order$2D+1$, then the total distance of$G$is at most the total distance of the cycle of the same order. In this note, we prove that this conjecture is true for 2-connected graphs.
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2012 ◽
Vol 21
(1-2)
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pp. 107-111
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2018 ◽
Vol 12
(2)
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pp. 297-317
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