On k-total distance degrees and k-total Wiener polarity index


Ediz S., Çiftçi İ., Cancan M., Farahani M. R.

JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES, vol.42, no.7, pp.1469-1477, 2021 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 7
  • Publication Date: 2021
  • Doi Number: 10.1080/02522667.2021.1896652
  • Journal Name: JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES
  • Journal Indexes: Emerging Sources Citation Index
  • Page Numbers: pp.1469-1477
  • Keywords: k-total distance degree, Wiener polarity index, k-total Wiener polarity index, ZERO DIVISOR GRAPH, ZAGREB INDEXES, MATRICES

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.