On zeroth-order general Randić index of conjugated unicyclic graphs

2007 ◽  
Vol 43 (2) ◽  
pp. 737-748 ◽  
Author(s):  
Hongbo Hua ◽  
Maolin Wang ◽  
Hongzhuan Wang
2007 ◽  
Vol 155 (8) ◽  
pp. 1044-1054 ◽  
Author(s):  
Yumei Hu ◽  
Xueliang Li ◽  
Yongtang Shi ◽  
Tianyi Xu

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 98 ◽  
Author(s):  
Muhammad Kamran Jamil ◽  
Ioan Tomescu ◽  
Muhammad Imran ◽  
Aisha Javed

For a graph G without isolated vertices, the inverse degree of a graph G is defined as I D ( G ) = ∑ u ∈ V ( G ) d ( u ) − 1 where d ( u ) is the number of vertices adjacent to the vertex u in G. By replacing − 1 by any non-zero real number we obtain zeroth-order general Randić index, i.e., 0 R γ ( G ) = ∑ u ∈ V ( G ) d ( u ) γ , where γ ∈ R − { 0 } . Xu et al. investigated some lower and upper bounds on I D for a connected graph G in terms of connectivity, chromatic number, number of cut edges, and clique number. In this paper, we extend their results and investigate if the same results hold for γ < 0 . The corresponding extremal graphs have also been identified.


2022 ◽  
Vol 306 ◽  
pp. 7-16
Author(s):  
Monther Rashed Alfuraidan ◽  
Kinkar Chandra Das ◽  
Tomáš Vetrík ◽  
Selvaraj Balachandran

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