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

Abstract

The general sum-connectivity index of a graph $G$ is defined as ${\chi }_{\alpha }(G)={\sum }_{uv\in E(G)}(d_u+d_v{)}^{\alpha }$ where $d_u$ is degree of the vertex $u\in V(G)$, $\alpha$ 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 ${\chi }_{\alpha }$ 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.

References in corpus (1)

• On the Extremal Graphs with Respect to Bond Incident Degree Indices