engleski

Two upper bounds on the weighted Harary indices

The paper is concerned with the weighted Harary indices, namely the multiplicatively weighted Harary index $H_M$ and the additively weighted Harary index $H_A$. For a simple connected graph $G$ with $n$ vertices, $m$ edges and $k$ cut edges, sharp upper bounds on $H_M(G)$ and $H_A(G)$ are derived and the corresponding extremal graphs are characterized. From one of the established bounds, a main result of the paper [X. Li, J.-B. Liu, \textit{; ; On the reciprocal degree distance of graphs with cut vertices or cut edges}; ; , Ars Comb. {; ; \bf 130}; ; , (2017) 303--318] follows instantly.

weighted Harary indices ; multiplicatively weighted Harary index ; additively weighted Harary index ; reciprocal degree distance ; cut edge

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