On the locating matrix of a graph and its spectral analysis

Abstract

We introduce a new matrix representation for a graph by defining the locating matrix $\mathbf{Lo}(G)$ of $G$. We define the locating eigenvalues, the locating spectrum, and locating energy of the graph and we calculate them for some standard graphs. We also obtain bounds for the locating energy for regular and strongly regular graphs.

Keywords

• Locating eigenvalues (of graph)
• Locating Spectrum (of graph)
• Locating energy (of graph)