On K-Total Distance Degrees and K-Total Wiener Polarity Index

Abstract

This study investigates the relationship between classical degree and recently defined k-distance degree, ve-degree and ev-degree concepts in graph theory. We firstly define the k-total distance degree notion and investigate its relation with Zagreb and Wiener polarity indices. One of the main relation is W-3*(T) = 1/2 M-1 (T) + W-p (T) where W-3* (T), M-1 (T) and W-p(T) denotes 3-total Wiener polarity index, the first Zagreb index and Wiener polarity index, respectively for any tree T.