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Journal of Applied Mathematics and Computing

Erschienen in:

01.06.2014 | Original Research

The Harary index of ordinary and generalized quasi-tree graphs

verfasst von: Kexiang Xu, Jinlan Wang, Hongshuang Liu

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2014

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Abstract

The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. The quasi-tree graph is a graph G in which there exists a vertex v∈V(G) such that G−v is a tree. In this paper, we presented the upper and lower bounds on the Harary index of all quasi-tree graphs of order n and characterized the corresponding extremal graphs. Moreover we defined the k-generalized quasi-tree graph to be a connected graph G with a subset V _k⊆V(G) where |V _k|=k such that G−V _k is a tree. And we also determined the k-generalized quasi-tree graph of order n with maximal Harary index for all values of k and the extremal one with minimal Harary index for k=2.

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Titel: The Harary index of ordinary and generalized quasi-tree graphs
verfasst von: Kexiang Xu
Jinlan Wang
Hongshuang Liu
Publikationsdatum: 01.06.2014
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2014
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-013-0727-4

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