Bounding the Mostar index
\v{S}tefko Miklavi\v{c}, Johannes Pardey, Dieter Rautenbach and, Florian Werner

TL;DR
This paper improves the upper bounds on the Mostar index of graphs, a measure related to vertex distances, and introduces a new parameter that provides tighter bounds, with implications for graph theory conjectures.
Contribution
The authors establish a sharper upper bound on the parameter $Mo^igstar(G)$, improving previous results and demonstrating its near-optimality, while also deriving bounds based on maximum degree.
Findings
Improved upper bound: $Mo^igstar(G) \\leq (\frac{2}{\sqrt{3}}-1)n^3$.
Bound depending on maximum degree: $Mo^igstar(G)$ expressed in terms of $\Delta$ and $n$.
Results are tight up to lower order terms.
Abstract
Do\v{s}li\'{c} et al. defined the Mostar index of a graph as , where, for an edge of , the term denotes the number of vertices of that have a smaller distance in to than to . They conjectured that for every graph of order . As a natural upper bound on the Mostar index, Geneson and Tsai implicitly consider the parameter . For a graph of order , they show that . We improve this bound to , which is best possible up to terms of lower order. Furthermore, we show that $Mo^\star(G)\leq…
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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research · Interconnection Networks and Systems
