The Square Graph of a Cycle Graph - Saha, Nabajit; Das, Manmohan (Communications in Mathematics and Applications, 2025)
The square graph of a cycle graph \(C_n\) is a graph consisting of the same set of vertex as in \(C_n\) and two different vertices are considered adjacent if their distance in \(C_n\) is at most two. We denote the square graph of a cycle graph \(C_n\) by \(C^2_n\). In this article, we first show that the square graph \(C^2_n\) is a 4-regular graph for \(n≥5\) and then discuss various graphical properties such as the spectrum, Laplacian spectrum of \(C^2_n\), tree number, energy and, finally, the vertex coloring of \(C^2_n\).