Harary index of the K-th power of a graph

Guifu Su; Liming Xiong; Ivan Gutman

doi:10.2298/AADM121130024S

Harary index of the K-th power of a graph

Guifu Su^*
, Liming Xiong
, Ivan Gutman

^*Corresponding author for this work

Beijing Institute of Technology
University of Georgia
University of Kragujevac

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

11 Citations (Scopus)

Abstract

The k-th power of a graph G, denoted by G^k, is a graph with the same set of vertices as G, such that two vertices are adjacent in G^k if and only if their distance in G is at most k. The Harary index H is the sum of the reciprocal distances of all pairs of vertices of the underlying graph. Lower and upper bounds on H(G^k) are obtained. A Nordhaus-Gaddum type inequality for H(G^k) is also established.

Original language	English
Pages (from-to)	94-105
Number of pages	12
Journal	Applicable Analysis and Discrete Mathematics
Volume	7
Issue number	1
DOIs	https://doi.org/10.2298/AADM121130024S
Publication status	Published - Apr 2013
Externally published	Yes

Keywords

Harary index
Nodrhaus-Gaddum type inequality
k-th power of graph

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10.2298/AADM121130024S

Cite this

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KW - Nodrhaus-Gaddum type inequality

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Harary index of the K-th power of a graph

Abstract

Keywords

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