Malaysian Journal of Mathematical Sciences, September 2026, Vol. 20, No. 3
A New Class of Almost Controllable Graphs
Alshamary, B. and An?eli?, M.
Corresponding Email: bader231.ku@ku.edu.kw
Received date: 18 July 2025
Accepted date: 4 January 2026
Abstract:
A graph $G$ is called a chain graph if it contains none of the graphs $\{2K_2, C_3, C_5\}$ as induced subgraphs. It is said to be almost controllable if it has exactly one non-main eigenvalue, that is, precisely one eigenvalue whose corresponding eigenspace is orthogonal to the all-ones vector. Within the class of chain graphs, we identify new families of graphs exhibiting this almost controllable property.
Keywords: chain graphs; main or non-main eigenvalues; almost controllable graphs.
