Year: 2018
Type: preprint
Abstract: The general sum-connectivity index of a graph $G$ is defined as $χ_α(G)= \sum_{uv\in E(G)} (d_u + d_{v})^α$ where $d_{u}$ is degree of the vertex $u\in V(G)$, $α$ 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 $χ_α$ values from a certain collection of polyomino chain graphs is solved for $α<0$. The obtained results together with already known results (concerning extremum values of polyomino chain graphs) give the complete solution of the aforementioned problem.
Source: arXiv (Cornell University)
Authors: Ali, Akbar, Idrees, Tahir
Institutions: University of Ha'il, University of Management and Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2791715533