Two upper bounds for the degree distances of four sums of graphs

Mingqiang An; Liming Xiong; Kinkar Ch Das

doi:10.2298/FIL1403579A

Two upper bounds for the degree distances of four sums of graphs

Mingqiang An, Liming Xiong, Kinkar Ch Das

Department of Mathematics

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

13 Scopus citations

Abstract

The degree distance (DD), which is a weight version of theWiener index, defined for a connected graph G as vertex-degree-weighted sum of the distances, that is, DD(G) = S∑_{u,v}⊆V(G)[d_G(u) +d_G(v)]d(u,v|G), where d_G(u) denotes the degree of a vertex u in G and d(u,v|G) denotes the distance between two vertices u and v in G: In this paper, we establish two upper bounds for the degree distances of four sums of two graphs in terms of other indices of two individual graphs.

Original language	English
Pages (from-to)	579-590
Number of pages	12
Journal	Filomat
Volume	28
Issue number	3
DOIs	https://doi.org/10.2298/FIL1403579A
State	Published - 2014

Keywords

Bounds
Degree distance
Distance (in graphs)
Sums of graphs

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10.2298/FIL1403579A

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T1 - Two upper bounds for the degree distances of four sums of graphs

AU - An, Mingqiang

AU - Xiong, Liming

AU - Das, Kinkar Ch

PY - 2014

Y1 - 2014

N2 - The degree distance (DD), which is a weight version of theWiener index, defined for a connected graph G as vertex-degree-weighted sum of the distances, that is, DD(G) = S∑{u,v}⊆V(G)[dG(u) +dG(v)]d(u,v|G), where dG(u) denotes the degree of a vertex u in G and d(u,v|G) denotes the distance between two vertices u and v in G: In this paper, we establish two upper bounds for the degree distances of four sums of two graphs in terms of other indices of two individual graphs.

AB - The degree distance (DD), which is a weight version of theWiener index, defined for a connected graph G as vertex-degree-weighted sum of the distances, that is, DD(G) = S∑{u,v}⊆V(G)[dG(u) +dG(v)]d(u,v|G), where dG(u) denotes the degree of a vertex u in G and d(u,v|G) denotes the distance between two vertices u and v in G: In this paper, we establish two upper bounds for the degree distances of four sums of two graphs in terms of other indices of two individual graphs.

KW - Bounds

KW - Degree distance

KW - Distance (in graphs)

KW - Sums of graphs

UR - https://www.scopus.com/pages/publications/84904387978

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DO - 10.2298/FIL1403579A

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SN - 0354-5180

VL - 28

SP - 579

EP - 590

JO - Filomat

JF - Filomat

IS - 3

ER -

Two upper bounds for the degree distances of four sums of graphs

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