Affiliation:
1. Faculty of Electronics Engineering, University of Niš, Niš, Serbia
Abstract
Let G = (V, E), V = {v1, v2,..., vn}, be a simple connected graph of
order n and size m, without isolated vertices. Denote by d1 ? d2 ?... ?
dn, di = d(vi) a sequence of vertex degrees of G. The general zeroth-order
Randic index is defined as 0R?(G) = ?ni =1 d?i, where ? is an arbitrary
real number. The corresponding general zeroth-order Randic coindex is
defined via 0R??(G) = ?ni=1(n?1?di)d?i. Some new bounds for the general
zeroth-order Randic coindex and relationship between 0R??(G?) and 0R???1(G?)
are obtained. For a particular values of parameter ? a number of new bounds
for different topological coindices are obtained as corollaries.
Publisher
National Library of Serbia
Reference22 articles.
1. T. Došlić, Vertex-weighted Wiener polynomials for composite graphs, Ars Math. Contemp. 1 (2008) 66-80.
2. D. D. Ismailescu, D. Stefanica, Minimizer graphs for a class of extremal problems, J. Graph Theory 39 (2002) 230-240.
3. T. Došlić, T. Reti, D. Vukičević, On the vertex degree indices of connected graphs, Chem. Phys. Lett. 512 (2011) 283-286.
4. I. Gutman, On coindices of graphs and their complements, Appl. Math. Comput. 305 (2017) 161-165.
5. Y. Hu, X. Li, Y. Shi, T. Xu, I. Gutman, On molecular graphs with smallest and greatest zeroth-order general Randić index, MATCH Commun. Math. Comput. Chem. 54 (2005) 425-434.