## Abstract

The degree distance of a graph * G * is D'(G)=(1/2)∑ ^{ n } _{ i=1 } ∑ * ^{ n } *

_{ j= 1 }(

*d*)L

_{ i }+d_{ j }_{ i ,j }, where

*d*and

_{ i }*d*

_{ j }are the degrees of vertices

*v*, and

_{ i }, v_{ j }∈ V (G)*L*

_{ i,j }is the distance between them. The Wiener index is defined as

*W(G)*=(1/2)∑

^{ n }

*i*

_{ =1 }∑

^{ n }*L*

_{ j-1 }*. An elegant result (Gutman; Klein, Mihalic, Plavsic and Trinajstic) is known regarding their correlation, that*

_{ i, j }*D'(T)*=

*4W(T)*-

*n*(

*n*-1)for a tree

*T*with

*n*vertices. In this note, we extend this study for more general graphs that have frequent appearances in the study of these indices. In particular, we develop a formula regarding their correlation, with an error term that is presented with explicit formula as well as sharp bounds for unicyclic graphs and cacti with given parameters.

Original language | American English |
---|---|

Journal | Open Journal of Discrete Mathematics |

Volume | 2 |

DOIs | |

State | Published - Oct 1 2012 |

## Keywords

- Degree distance
- Wiener index
- Cacti

## DC Disciplines

- Education
- Mathematics