Cacti with Extremal PI Index

oleh: Chunxiang Wang, Shaohui Wang, Bing Wei

Format: Article
Diterbitkan: University of Isfahan 2016-12-01

Deskripsi

The vertex PI index PI(G)=∑ xy∈E(G) [n xy (x)‎+‎n xy (y)] PI(G)=∑xy∈E(G)[nxy(x)‎+‎nxy(y)] is a distance-based molecular structure descriptor‎, ‎where n xy (x) nxy(x) denotes the number of vertices which are closer to the vertex x x than to the vertex y y and which has been the considerable research in computational chemistry dating back to Harold Wiener in 1947‎. ‎A connected graph is a cactus if any two of its cycles have at most one common vertex‎. ‎In this paper‎, ‎we completely determine the extremal graphs with the greatest and smallest vertex PI indices mong all cacti with a fixed number of vertices‎. ‎As a consequence‎, ‎we obtain the sharp bounds with corresponding extremal cacti and extend a known result‎.