paper

On the first three minimum Mostar indices of tree-like phenylenes

arXiv:2103.04018 · doi:10.1007/s12190-021-01677-9

Abstract

Let $G = (V_{G}, E_{G})$ be a simple connected graph with its vertex set $V_{G}$ and edge set $E_{G}$ . The Mostar index $M o (G)$ was defined as $M o (G) = e = uv \in E (G) \sum ∣ n_{u} - n_{v} ∣$ , where $n_{u}$ (resp., $n_{v}$ ) is the number of vertices whose distance to vertex $u$ (resp., $v$ ) is smaller than the distance to vertex $v$ (resp., $u$ ). In this study, we determine the first three minimum Mostar indices of tree-like phenylenes and characterize all the tree-like phenylenes attaining these values. At last, we give some numerical examples and discussion.

17 pages, 6 figures