A Note on the Zeroth-order General Randić Index of Polygonal Cacti

Ye, Jiachang; Yao, Yuedan

doi:10.30538/psrp-odam2018.0001

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2020

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“…Jamil et al [21] investigated the extremal graphs of k-generalized quasi trees for zeroth-order general Randić index. For further results we refer to [22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Some Bounds on Zeroth-Order General Randić Index

et al. 2020

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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.

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