Please use this identifier to cite or link to this item: https://scidar.kg.ac.rs/handle/123456789/8853
Title: The variation of the Randić index with regard to minimum and maximum degree
Authors: Milivojević M.
Pavlović, Ljiljana
Issue Date: 2017
Abstract: © 2016 Elsevier B.V. The variation of the Randić index R′(G) of a graph G is defined by  R′(G)=∑uv∈E(G)[formula presented], where d(u) is the degree of vertex u and the summation extends over all edges uv of G. Let G(k,n) be the set of connected simple n-vertex graphs with minimum vertex degree k. In this paper we found in G(k,n) graphs for which the variation of the Randić index attains its minimum value. When k≤[formula presented] the extremal graphs are complete split graphs Kk,n−k∗, which have only vertices of two degrees, i.e. degree k and degree n−1, and the number of vertices of degree k is n−k, while the number of vertices of degree n−1 is k. For k≥[formula presented] the extremal graphs have also vertices of two degrees k and n−1, and the number of vertices of degree k is [formula presented]. Further, we generalized results for graphs with given maximum degree.
URI: https://scidar.kg.ac.rs/handle/123456789/8853
Type: article
DOI: 10.1016/j.dam.2016.09.010
ISSN: 0166-218X
SCOPUS: 2-s2.0-84996521019
Appears in Collections:Faculty of Science, Kragujevac

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