A Relation Between Wiener Index and Mostar Index for Daisy Cubes

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 over 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.