A relation between Wiener index and Mostar index for daisy cubes

TL;DR

This paper establishes a mathematical relationship between Wiener and Mostar indices specifically for daisy cubes, a class of graphs relevant in chemical graph theory, providing explicit formulas for these indices.

Contribution

The paper introduces a new relation linking Wiener and Mostar indices for daisy cubes, expanding understanding of their structural properties in graph theory and chemistry.

Findings

Wiener and Mostar indices are related by 2W(G) - Mo(G) = |V(G)||E(G)| for daisy cubes.

Explicit formulas for Wiener and Mostar indices of daisy cubes are provided.

Daisy cubes include Fibonacci and Lucas cubes, relevant in chemical graph theory.

Abstract

Daisy cubes are a class of isometric subgraphs of the hypercubes Q n. Daisy cubes include some previously well known families of graphs like Fibonacci cubes and Lucas cubes. Moreover they appear in chemical graph theory. Two distance invariants, Wiener and Mostar indices, have been introduced in the context of the mathematical chemistry. The Wiener index W (G) is the sum of distance between all unordered pairs of vertices of a graph G. The Mostar index Mo(G) is a measure of how far G is from being distance balanced. In this paper we establish that the Wiener and the Mostar indices of a daisy cube G are linked by the relation 2W (G) -- Mo(G) = |V (G)||E(G)|. We give also an expression of Wiener and Mostar indices for daisy cubes.