CACTI WITH EXTREMAL PI INDEX

By Chunxiang Wang, Shaohui Wang, Bing Wei. 2016

52 citations recorded by the source corpus.

The vertex PI index $PI(G) = sum_{xy in E(G)} [n_{xy}(x)‎ + ‎n_{xy}(y)]$ is a distance-based molecular structure descriptor‎, ‎where $n_{xy}(x)$ denotes the number of vertices which are closer to the vertex $x$ than to the vertex $y$ 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.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bcbde0f1a2439687d9e2292edc7a0b3026d9a7d4

Citations in the corpus

• Distance‐based topological descriptors for measuring the π‐electronic energy of benzenoid hydrocarbons with applications to carbon nanotubes (2020, unknown): “For a graph Γ , the PI index is defined as follows: Wang et al 31 studied the extremal cacti graphs with respect to the PI index.”