On the Extremal Mostar Indices of Trees with a Given Segment Sequence

作者：Deng, Kecai; Li, Shuchao^*

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2022, 45(2): 593-612.

DOI：10.1007/s40840-021-01208-6

• Segment sequence
• Mostar index

Given a graph G and an edge e = xy in G, let n(x) (e) and n(y)(e) be the number of vertices that have the distance to x less than that to y, and the number of vertices that have the distance to y less than that to x, respectively. The contribution of e is defined as vertical bar n(x) (e) - n(y) (e)vertical bar. The Mostar index of G is the sum of all edge contributions in G. A segment in a given tree T is a path, each of whose inner vertices has degree exactly 2, and none of whose two ends has the degree 2. The segment sequence of T is the length sequence of all segments in T. In this paper, we focus on the tree set with a fixed segment sequence, and the tree set with a fixed size together with a fixed segment number. We completely determine the graphs with the greatest Mostar index among the two sets, respectively. The graphs with the least Mostar index among the second set are also identified.