given size of matching
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2018 ◽  
Vol 68 (9) ◽  
pp. 1779-1791 ◽  
Author(s):  
Li Su ◽  
Liying Kang ◽  
Honghai Li ◽  
Erfang Shan

Filomat ◽  
2014 ◽  
Vol 28 (2) ◽  
pp. 421-428 ◽  
Author(s):  
Yan Zhu ◽  
Renying Chang

The harmonic index H(G) of a graph G is defined as the sum of weights 2/ d(u)+d(v) of all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this paper, we first present a sharp lower bound on the harmonic index of bicyclic conjugated molecular graphs (bicyclic graphs with perfect matching). Also a sharp lower bound on the harmonic index of bicyclic graphs is given in terms of the order and given size of matching.


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