A note on polyomino chains with extremum general sum-connectivity index

DOI10.22049/CCO.2020.26866.1153zbMath1488.05072arXiv1803.04657OpenAlexW3209957700MaRDI QIDQ4957542

No author found.

Publication date: 9 September 2021

Abstract: The general sum-connectivity index of a graph $G$ is defined as $ch{i}_{alpha}(G)=su{m}_{uvinE(G)}(d_u+d_v{)}^{alpha}$ where $d_u$ is degree of the vertex $uinV(G)$, $alpha$ is a real number different from $0$ and $uv$ is the edge connecting the vertices $u,v$. In this note, the problem of characterizing the graphs having extremum $ch{i}_{alpha}$ values from a certain collection of polyomino chain graphs is solved for $alpha<0$. The obtained results together with already known results (concerning extremum values of polyomino chain graphs) give the complete solution of the aforementioned problem.

Full work available at URL: https://arxiv.org/abs/1803.04657

zbMATH Keywords

Randić indexpolyomino chaingeneral sum-connectivity index

Mathematics Subject Classification ID

Connectivity (05C40) Vertex degrees (05C07) Graphical indices (Wiener index, Zagreb index, Randi? index, etc.) (05C09)

Cites Work

• Bounds for the general sum-connectivity index of composite graphs
• Extremal polyomino chains with respect to Zagreb indices
• The general connectivity indices of fluoranthene-type benzenoid systems
• On a novel connectivity index
• On the extremal graphs with respect to bond incident degree indices
• Randić index and information
• On the extremal graphs for general sum-connectivity index \((\chi_{{}_\alpha})\) with given cyclomatic number when \(\alpha > 1\)
• Bond incident degree (BID) indices of polyomino chains: a unified approach
• Sharp bounds for the general sum-connectivity indices of transformation graphs
• Minimum general sum-connectivity index of trees and unicyclic graphs having a given matching number
• On the general sum-connectivity index of trees with given number of pendent vertices
• On maximal resonance of polyomino graphs
• The number of Kekulé structures of polyominos on the torus
• On general sum-connectivity index
• The minimum general sum-connectivity index of trees with given matching number
• Proof of a conjecture concerning maximum general sum-connectivity index \(\chi_\alpha\) of graphs with given cyclomatic number when \(1 < \alpha < 2\)
• General sum-connectivity index, general product-connectivity index, general Zagreb index and coindices of line graph of subdivision graphs
• Series expansion of the directed percolation probability
• An alternative but short proof of a result of Zhu and Lu concerning general sum-connectivity index
• Correcting a paper on the Randi{\'c} and geometric--arithmetic indices
• Some new bounds on the general sum--connectivity index
• F-index and hyper-Zagreb index of four new tensor products of graphs and their complements
• More results on extremum Randic indices of (molecular) trees
• Inverse degree, Randic index and harmonic index of graphs
• The hyper-Zagreb index of cacti with perfect matchings
• Extremal polyomino chains with respect to general Randić index
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

Related Items (5)

The spectral radius of signless Laplacian matrix and sum-connectivity index of graphs ⋮ Sharp bounds for the second-order general connectivity index of hexagonal chains ⋮ Expected value for the \(k\)-distance degree index of a graph ⋮ On the maximum general sum-connectivity index of trees with a fixed order and maximum degree ⋮ Extremum sum-connectivity index of trees and unicyclic graphs

Uses Software

• GRAFFITI

This page was built for publication: A note on polyomino chains with extremum general sum-connectivity index