Möbius inversion on a poset of a graph and its acyclic subgraphs
type: Item
instance of: scholarly article
title: Möbius inversion on a poset of a graph and its acyclic subgraphs
zbMATH Open document ID: 0857.05089
DOI: 10.1016/0166-218X(95)00007-E
published in: Discrete Applied Mathematics
publication date: 1997-03-06T00:00:00Z
review text: In the frame of the cluster expansion concept, a molecular property \(X(G)\) is formally expanded into a sum of contributions from all molecular fragments \(G'\) of \(G\), determining cluster expansion in chemistry. For expressing the resonance energy in molecules the Möbius function for the partially ordered set of a connected cyclic graph \(G\) and its acyclic subgraphs \(G'\) is useful. Here the authors determine this Möbius function using terms of graph theory as follows: \[ \mu[G',G]=-\prod_{v_i\in G-G'}(1-d_i), \] where \(d_i\) denotes the number of edges by which \(v_i\) is linked to vertices in \(G'\).
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 92E10
zbMATH DE Number: 897414
zbMATH Keywords: cluster expansion in chemistry
zbMATH Keywords: Möbius function
zbMATH Keywords: acyclic subgraphs
author: Darko Babić
author: Nenad Trinajstić
reviewed by: Michael Hager
MaRDI profile type: Publication
cites work: Enumeration of acyclic walks in a graph
cites work: Graph theory and statistical physics
cites work: On the foundations of combinatorial theory I. Theory of M�bius Functions
cites work: Q5607111
description: scientific article; zbMATH DE number 897414