2011/04/21 by Aleksandar Ili ' c, Aleksandar Ili\' c, c, Aleksandar Ili\' +3
Chemistry · Computer Science · Mathematics · #05C12 #92E10 #Combinatorics (math.CO) #Computational Drug Discovery Methods #FOS: Mathematics #Graph theory and applications #Synthesis and Properties of Aromatic Compounds #math.CO #msc:05C12 #msc:92E10
paper · pdf · doi:10.48550/arxiv.1104.4259
13 page, 1 figure
arxiv created 2011/04/21 · openalex publication_date 2011/04/21 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The vertex PI index is a distance--based molecular structure descriptor, that recently found numerous chemical applications. In order to increase diversity of this topological index for bipartite graphs, we introduce weighted version defined as PIw (G) = ∑e = uv ∈ E (deg (u) + deg (v)) (nu (e) + nv (e)), where deg (u) denotes the vertex degree of u and nu (e) denotes the number of vertices of G whose distance to the vertex u is smaller than the distance to the vertex v. We establish basic properties of PIw (G), and prove various lower and upper bounds. In particular, the path Pn has minimal, while the complete tripartite graph Kn/3, n/3, n/3 has maximal weighed vertex PI index among graphs with n vertices. We also compute exact expressions for the weighted vertex PI index of the Cartesian product of graphs. Finally we present modifications of two inequalities and open new perspectives for the future research.