Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4949800 | Discrete Applied Mathematics | 2017 | 8 Pages |
Abstract
The variation of the RandiÄ index Râ²(G) of a graph G is defined by Râ²(G)=âuvâE(G)1max{d(u),d(v)}, 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 RandiÄ index attains its minimum value. When kâ¤n2 the extremal graphs are complete split graphs Kk,nâkâ, which have only vertices of two degrees, i.e. degree k and degree nâ1, and the number of vertices of degree k is nâk, while the number of vertices of degree nâ1 is k. For kâ¥n2 the extremal graphs have also vertices of two degrees k and nâ1, and the number of vertices of degree k is n2. Further, we generalized results for graphs with given maximum degree.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Milica MilivojeviÄ, Ljiljana PavloviÄ,