The atom-bond connectivity index of catacondensed polyomino graphs
type: Item
instance of: scholarly article
title: The atom-bond connectivity index of catacondensed polyomino graphs
zbMATH Open document ID: 1283.05148
DOI: 10.1155/2013/598517
author: Jinsong Chen
author: Qiaoliang Li
author: Jianping Liu
published in: Discrete Dynamics in Nature and Society
publication date: 2013-06-13T00:00:00Z
review text: Summary: Let \(G = (V, E)\) be a graph. The atom-bond connectivity (ABC) index is defined as the sum of weights \(((d_u + d_v - 2)/d_ud_v)^{1/2}\) over all edges \(uv\) of \(G\), where \(d_u\) denotes the degree of a vertex \(u\) of \(G\). In this paper, we give the atom-bond connectivity index of the zigzag chain polyomino graphs. Meanwhile, we obtain the sharp upper bound on the atom-bond connectivity index of catacondensed polyomino graphs with \(h\) squares and determine the corresponding extremal graphs.
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 05B50
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 6175096
zbMATH Keywords: atom-bond connectivity index
zbMATH Keywords: catacondensed polyomino graphs
zbMATH Keywords: extremal graphs
Wikidata QID: Q58921673
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/598517
OpenAlex ID: W1964326816
cites work: Maximum Zagreb index, minimum hyper-Wiener index and graph connectivity
cites work: Q4903402
cites work: Q3556939
cites work: Q4903401
cites work: Q4903454
cites work: Q4903407
cites work: The atom-bond connectivity index of chemical bicyclic graphs
cites work: Some upper bounds for the atom-bond connectivity index of graphs
cites work: Atom-bond connectivity index of trees
cites work: Further results on atom-bond connectivity index of trees
cites work: Combinatorial properties of polyominoes
cites work: Chessboard domination problems
cites work: Perfect matchings of generalized polyomino graphs
description: scientific article; zbMATH DE number 6175096