Reciprocal product–degree distance of graphs

Guifu Su; Liming Xiong; Ivan Gutman; Lan Xu

doi:10.2298/FIL1608217S

Reciprocal product–degree distance of graphs

Guifu Su, Liming Xiong, Ivan Gutman, Lan Xu

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We investigate a new graph invariant named reciprocal product–degree distance, defined as: (Formula Presented) where deg(v) is the degree of the vertex v, and dist(u; v) is the distance between the vertices u and v in the underlying graph. RDD* is a product–degree modification of the Harary index. We determine the connected graph of given order with maximum RDD*-value, and establish lower and upper bounds for RDD*. Also a Nordhaus–Gaddum–type relation for RDD* is obtained.

Original language	English
Pages (from-to)	2217-2231
Number of pages	15
Journal	Filomat
Volume	30
Issue number	8
DOIs	https://doi.org/10.2298/FIL1608217S
Publication status	Published - 2016

Keywords

Degree distance
Distance (in graph)
Product–degree distance
Reciprocal degree distance
Reciprocal product-degree distance

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10.2298/FIL1608217S

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T1 - Reciprocal product–degree distance of graphs

AU - Su, Guifu

AU - Xiong, Liming

AU - Gutman, Ivan

AU - Xu, Lan

PY - 2016

Y1 - 2016

N2 - We investigate a new graph invariant named reciprocal product–degree distance, defined as: (Formula Presented) where deg(v) is the degree of the vertex v, and dist(u; v) is the distance between the vertices u and v in the underlying graph. RDD* is a product–degree modification of the Harary index. We determine the connected graph of given order with maximum RDD*-value, and establish lower and upper bounds for RDD*. Also a Nordhaus–Gaddum–type relation for RDD* is obtained.

AB - We investigate a new graph invariant named reciprocal product–degree distance, defined as: (Formula Presented) where deg(v) is the degree of the vertex v, and dist(u; v) is the distance between the vertices u and v in the underlying graph. RDD* is a product–degree modification of the Harary index. We determine the connected graph of given order with maximum RDD*-value, and establish lower and upper bounds for RDD*. Also a Nordhaus–Gaddum–type relation for RDD* is obtained.

KW - Degree distance

KW - Distance (in graph)

KW - Product–degree distance

KW - Reciprocal degree distance

KW - Reciprocal product-degree distance

UR - http://www.scopus.com/inward/record.url?scp=85006058457&partnerID=8YFLogxK

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DO - 10.2298/FIL1608217S

M3 - Article

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VL - 30

SP - 2217

EP - 2231

JO - Filomat

JF - Filomat

IS - 8

ER -

Reciprocal product–degree distance of graphs

Abstract

Keywords

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