On the degree distance of a graph

Authors:
P. Dankelmann;I. Gutman;S. Mukwembi;H. C. Swart
Affiliations:
University of KwaZulu-Natal, Durban, South Africa;University of Kragujevac, Kragujevac, Serbia;University of KwaZulu-Natal, Durban, South Africa;University of KwaZulu-Natal, Durban, South Africa
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 5
Cited 4

Molecular topological index

Journal of Chemical Information & Computer Sciences
An upper bound on the sum of squares of degrees in a graph

Discrete Mathematics
Semi extremal properties of the degree distance of a graph

Discrete Applied Mathematics
Note: Unicyclic and bicyclic graphs having minimum degree distance

Discrete Applied Mathematics
Note: The minimum degree distance of graphs of given order and size

Discrete Applied Mathematics

Degree distance of unicyclic and bicyclic graphs

Discrete Applied Mathematics
On the first geometric-arithmetic index of graphs

Discrete Applied Mathematics
On the reciprocal degree distance of graphs

Discrete Applied Mathematics
Degree distance and vertex-connectivity

Discrete Applied Mathematics

Quantified Score

Hi-index	0.04

Visualization

Abstract

If G is a connected graph with vertex set V, then the degree distance of G, D^'(G), is defined as @?"{"u","v"}"@?"V(degu+degv)d(u,v), where degw is the degree of vertex w, and d(u,v) denotes the distance between u and v. We prove the asymptotically sharp upper bound D^'(G)@?14nd(n-d)^2+O(n^7^/^2) for graphs of order n and diameter d. As a corollary we obtain the bound D^'(G)@?127n^4+O(n^7^/^2) for graphs of order n. This essentially proves a conjecture by Tomescu [I. Tomescu, Some extremal properties of the degree distance of a graph, Discrete Appl. Math. (98) (1999) 159-163].