2021
DOI: 10.46298/dmtcs.6956
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Wiener index in graphs with given minimum degree and maximum degree

Abstract: Let $G$ be a connected graph of order $n$.The Wiener index $W(G)$ of $G$ is the sum of the distances between all unordered pairs of vertices of $G$. In this paper we show that the well-known upper bound $\big( \frac{n}{\delta+1}+2\big) {n \choose 2}$ on the Wiener index of a graph of order $n$ and minimum degree $\delta$ [M. Kouider, P. Winkler, Mean distance and minimum degree. J. Graph Theory 25 no. 1 (1997)] can be improved significantly if the graph contains also a vertex of large degree. Specifically, we … Show more

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“…It follows from Lemma 5 that the term a i k + c i k is maximised, subject to ( 9) and (10), if a i = n + 1 − i − l−i j=1 m j and c i = i + 1. Since by (9) we have (n…”
Section: Considering All Other Possibilities We Find the Values Of D ...mentioning
confidence: 99%
“…It follows from Lemma 5 that the term a i k + c i k is maximised, subject to ( 9) and (10), if a i = n + 1 − i − l−i j=1 m j and c i = i + 1. Since by (9) we have (n…”
Section: Considering All Other Possibilities We Find the Values Of D ...mentioning
confidence: 99%