A Relation between D-Index and Wiener Index for r-Regular Graphs

For any two distinct vertices u and v in a connected graph G, let lPu,v=lP be the length of u−v path P and the D–distance between u and v of G is defined as: dDu,v=minplP+∑∀y∈VPdeg y, where the minimum is taken over all u−v paths P and the sum is taken over all vertices of u−v path P. The D-index of...

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Bibliographic Details
Published in:	International journal of mathematics and mathematical sciences Vol. 2020; no. 2020; pp. 1 - 6
Main Authors:	Ali, Ahmed Mohammed, Aziz, Asmaa Salah
Format:	Journal Article
Language:	English
Published:	Cairo, Egypt Hindawi Publishing Corporation 2020 Hindawi John Wiley & Sons, Inc Hindawi Limited
Subjects:	Apexes Decision trees Graph theory Graphs
Online Access:	Get full text
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Summary:	For any two distinct vertices u and v in a connected graph G, let lPu,v=lP be the length of u−v path P and the D–distance between u and v of G is defined as: dDu,v=minplP+∑∀y∈VPdeg y, where the minimum is taken over all u−v paths P and the sum is taken over all vertices of u−v path P. The D-index of G is defined as WDG=1/2∑∀v,u∈VGdDu,v. In this paper, we found a general formula that links the Wiener index with D-index of a regular graph G. Moreover, we obtained different formulas of many special irregular graphs.
ISSN:	0161-1712 1687-0425
DOI:	10.1155/2020/6937863