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Erschienen in:
2019 | OriginalPaper | Buchkapitel
14. A Note on the Upper Bound of Average Distance via Irregularity Index
verfasst von : Nihat Akgunes, Ismail Naci Cangul, Ahmet Sinan Cevik
Erschienen in: Mathematical Methods in Engineering
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Abstract
In this paper, we use a technique introduced by Dankelmann and Entringer (J Graph Theory 33:1–13, 2000) to obtain a strengthening of an old classical theorem by Kouider and Winkler (J Graph Theory 25:95–99, 1997) on mean distance and minimum degree. It is known that the mean distance and the average distance are the same parameters. To be more detailed, we will prove that if G is a connected graph of order n with minimum degree δ, then the average distance of G does not exceed where t is the irregularity index (that is the number of distinct terms of the degree sequence of G). We note that the irregularity index has been recently defined and studied in the paper (Mukwembi, Appl Math Lett 25:175–178, 2012).
$$\displaystyle \frac {n-t+1}{\delta +1}+1, $$