ARTICLE
TITLE

Zeroth-order general Randic index of trees with given distance k-domination number

SUMMARY

The zeroth-order general Randic index of a graph G is defined as Ra(G)=?v ? V(G)dGa(v), where a ? R, V(G) is the vertex set of G and dG(v) is the degree of a vertex v in G. We obtain bounds on the zeroth-order general Randic index for trees of given order and distance k-domination number, where k = 1. Lower bounds are given for 0 < a < 1 and upper bounds are given for a < 0 and a > 1. All the extremal graphs are presented which means that our bounds are the best possible.

PAGES
pp. 247–257

 Articles related

Éva Czabarka,Peter Dankelmann,Trevor Olsen,László Székely    

Let G be a connected graph. If s(v) denotes the arithmetic mean of the distances from v to all other vertices of G, then the proximity, p(G), of G is defined as the smallest value of s(v) over a... see more


Doost Ali Mojdeh,Guoliang Hao,Iman Masoumi,Ali Parsian    

Given a simple graph G=(V,E) with maximum degree ?. Let (V0, V1, V2) be an ordered partition of V, where Vi = {v ? V : f(v)=i} for i = 0, 1 and V2 = {v ? V : f(v)=2}. A function f : V ? {0, 1, …, ??/2?+1} ... see more


B Basavanagoud,Praveen Jakkannavar,Shruti Policepatil    

A communication network can be considered to be highly vulnerable to disruption if the failure of few members (nodes or links) can result in no member’s being able to communicate with very many others. These communication networks can be modeled through ... see more


H.P. Le, D. Manevich, D. Plaumann    

Given a real algebraic curve, embedded in projective space, we study the computational problem of deciding whether there exists a hyperplane meeting the curve in real points only. More generally, given any divisor on such a curve, we may ask whether the ... see more

Revista: Le Matematiche

Ermanno Lanconelli    

Let H be a linear second order partial differential operator with non-negative characteristic form in a strip S ? R^N ×R. We assume that H as a fundamental solution, smooth out of its poles and bounded from above and from below by Gaussian kernels modele... see more

Revista: Le Matematiche